It seems like it could in fact be a valid sexuality type to be attracted exclusively to sex rather than gender, but the only common term that seems to describe this sexuality is "super straight" (when referencing the heterosexual form of this, while "super gay" might be an unused but equivalent term for the homosexual form) which carries harmful connotations that aren't inherently entailed by having this sexuality type - which I agree is not a broader sexual orientation like heterosexual/homosexual/bisexual/asexual etc, but is more like a "microlabel" such as demisexual, in that it's an additional descriptor that further specifies the exact nature of someone's individual sexual preferences/orientation. However, that also doesn't mean it needs to be considered as part of the LGBTQ+ community, as it's not a marginalized sexuality or identity - in fact I'm pretty sure it's one of the most common sexuality types there are, if not the most common. Especially due to how stigmatized or misunderstood this sexuality is, or that people feel it's invalid or tied to discrimination against LGBT people somewhat inseparably, there isn't much research on it, so it's possible that people who are attracted to gender are more common than people who are attracted to sex, but it could be the opposite.
I understand the history of this word is problematic as it was created by transphobes, and its perception is so heavily tied to those origins that it's considered a hateful ideology in itself. That's one reason the word needs a different replacement and a "fresh start". People are identifying as this sexuality without any bigoted ideas toward LGBT people, even being vocally pro-LGBT, but simply having no other word to describe their exact sexuality, and then using this word despite it having other connotations they don't agree with, because it's the closest word there is - and then being misunderstood and criticized for using it. It seems like replacing this word with a more well-intentioned one would actually serve to hinder those hateful ideologies from spreading (by stopping people from resorting to using it with no other alternative, as is happening a lot) and enable people to acknowledge the validity of all sexual preferences or orientations as distinct from any hateful rhetoric.
Additionally, the word itself carries problematic connotations linguistically - even if it wasn't tied to attempts to undermine LGBT rights movements - since it could be interpreted as implying that people who are attracted to people of the opposite gender regardless of sex are "less straight" than people who are only attracted to the opposite sex regardless of gender. This recalls the fairly backward arguments (or offensive jokes) that someone who is attracted to people who were born as the same sex as them but who identify/present as the opposite gender, is actually "secretly gay" or "in denial of being gay" due to that attraction and is not really straight - that, for example, a man who is capable of being attracted to either cis women as well as trans women is therefore somehow less straight or more gay (or bi) than one who is only attracted to cis women - and this may come across as undermining the validity of those people as truly being the gender they identify as, or in other words attempting to deny or downplay the fact that trans women are women and trans men are men.
But it must be understood that being attracted to sex rather than gender does not mean denying the validity of gender identities in any way. Someone can fully support the rights of and acknowledge the legitimacy of trans people, that trans women are women and trans men are men in full, etc. The reality is just that sex is something distinct from gender and some people are attracted to one or the other or both, but not necessarily both. It's not something that can be entirely rationalized or explained, just like why someone is attracted to men rather than women or vice versa, or any other sexuality. It's something that people just naturally feel. Some so-called "super straight" people, non-bigoted and well-meaning ones in search of a way to explain and justify their sexual choices, genuinely just don't feel attraction to people who were born as the same sex as them, even if those people identify as/present as the opposite gender to them, and even while still considering them to be women/men in alignment with their gender etc. For the homosexual equivalent, aka "super gay", some people also are only attracted to their own sex, and would not be attracted to someone who was born as the opposite sex even if they identified/presented as the same gender as them. How can we criticize someone for having a particular sexual preference or orientation like that? I'm not saying they're oppressed or anything for having that nature (for being gay, yes, not for being "super gay" or "super straight"), but it seems silly and harmful to not be able to distinguish between people who are attracted to sex and people who are attracted to gender - it also doesn't need to be necessarily words based on how it relates to a larger orientation (like "super straight" and "super gay") but rather an additional label that you can place on any sexuality which denotes whether your attraction is gender-based or sex-based, or either, or both. To say that that is somehow discriminating against individuals just by not being attracted to them in some way you can't change - despite fully respecting them - seems no different from suggesting that someone is discriminating against women or men just by not being attracted to them since that's their sexuality. Are gay men necessarily misogynists? Of course not. So why would people who are attracted to cis people (of a particular sex) and not trans people (of the opposite sex-assigned-at-birth to the sex they're attracted to) necessarily be transphobes? It seems like there would be further variations to this as well depending on how people's exact sexuality cashes out.
The fact we can't seem to talk about this without assuming people have bad intentions, lumping them together with other people via association fallacies, and strawmanning people as being bigoted while misunderstanding or deliberately misrepresenting their experience/position is silly. It's obviously a nuanced subject, and human sexuality is complex. There could well be some unrecognized validity to a differentiation between sex-based vs gender-based attraction, and it seems like it would benefit the LGBT rights movements to be able to acknowledge these kinds of experiences, of people who are genuinely supportive of LGBT, rather than immediately demonizing it without trying to understand it. Maybe we can have a bit of good faith here?
(Btw, I don't identify with the super straight label nor with the sexuality type it describes even with the bigotry removed, but I don't find it to be justified to criticize people for having this particular experience of sexual attraction, and think it deserves a proper unproblematic term, or multiple words related to the larger concept of sex vs gender based attraction).
Yeah, these are pretty good terms, especially for nonbinary people who don't have an exact term that factors in their own gender into their sexual attraction toward others (e.g. someone whose gender is neither male nor female but who is attracted to males or masculinity isn't really heterosexual nor homosexual, perhaps they are androsexual or androphilic). The only problem is that they could end up essentially running into the same questions about how they break down further into gender or sex or both or either. For example, gynesexual or gynephilic people doesn't really specify whether their attraction is gender-based or sex-based etc. The definitions also differ.
You described it as attraction to female or male bodies. Does this mean attraction to sex regardless of gender (as bodies are usually more tied to sex than they are gender identity) - and then, would it still apply if the body had been a different sex originally but was changed through operation? Or does it mean attraction to sex and gender combined (meaning they must have that body but also identify with the gender and present that way aka be cis)?
Additional definitions are listed as using both terms (gynephilia and gynesexual, for example, and the equivalents for the opposite gender/sex) as interchangeable and meaning attraction to either femininity, women, female presenting, or female identifying people, while other sources differentiate between gynephilia and gynesexual (as well as the male forms of both terms) and state that gynesexuality is attraction to femininity while gynephilia is attraction to people who identify as women. In that usage, gynesexuality could either apply to being attracted to anyone with any tangible femininity whatsoever, including femboys (even who are cis men), men crossdressing as women, trans women, cis women, or trans men (who were assigned female sex at birth, or perhaps only if they still had some feminine presentation or hadn't undergone sex change) - or it could exclude any of the above, since "femininity" is pretty vague. Gynephilia's meaning of attraction to people who identify as women (which is not the only listed definition, but almost sounds like the opposite of your definition for it, if we take female bodies to mean sex rather than gender), sounds like it's describing attraction to the female gender, possibly regardless of/independent of sex. That is, they could be attracted to a trans woman or a cis woman, but not to a trans man or cis man of any kind, regardless of female sex or presentation.
Needless to say, these terms are still pretty unclear without further specificity as to their most accepted meanings and also whether their attraction is rooted in gender, sex, both, either, or a broader and more vague concept of masculinity or femininity, and how exactly that's defined or formulated or how those attractions specifically manifest for people in terms of what kinds of feminity or masculinity they're attracted to (arguably many if not most or all people have a bit of both) or how much and of what kind is required to form an attraction.