Transgender

Trans women usually can't compete until having transitioned for a number of years, usually requiring hormone therapy for at least a year, and sometimes even requiring genital surgery before they can compete. They may or may not have any muscular advantage over cis women at that point, the theoretical advantages and disadvantages are due mostly to the skeletal system having been influenced by male puberty, resulting in longer and larger bones (which creates advantages in some competitions and disadvantages in others). However, there is significant variance in cis populations and more overlap between cis women and cis men in terms of height, limb length, hormone levels, etc. than most people realize, and there is no reason to think trans women have any kind of extreme or special advantage over the natural variation seen in cis women.

The idea that men have better hand-eye coordination and this gives trans women an advantage in fencing mistakes trans women for being men. The fact is that trans women are women not just for social reasons, trans women's brains are actually different than cis men's brains. Studies have found with respect to cognitive tasks like spatial reasoning relevant to hand-eye coordination, trans women are closer to cis women than cis men even before taking estrogen:

https://pmc.ncbi.nlm.nih.gov/articles/PMC6235900/

Among transgender individuals meeting criteria for [gender dysphoria], cortical thickness [80, 81], gray matter volume [80, 82], white matter microstructure [83, 84], structural connectivity [85], and corpus callosum shape [86] have been found to be more similar to cisgender control subjects of the same preferred gender compared with those of the same natal sex. Likewise, transgender individuals feature a unique pattern of connections in the resting state functional connectivity network that differ from those of their natal sex [87].

Performance on cognitive tasks by [trans women] and [trans men] prior to [hormone therapy] is often more congruent with gender identity. In most cases, investigators have focused on verbal and spatial tasks which display a clear sex bias. Verbal tasks show a female sex bias, while spatial tasks show a male sex bias. Multiple studies conclude that [trans women] perform significantly better on female-favoring verbal tests compared to cisgender male controls [88–90], whereas [trans men] perform significantly worse than cisgender female controls on verbal tests [90]. Measuring conceptual styles, [trans women] and [trans men] perform in congruence with their gender identity [91]. This suggests that the tendency towards “feminization” in [trans women] and “masculinization” in [trans men] is an innate quality unrelated to exogenous hormonal intervention, and more closely tied to brain development in transgender individuals.

We also know estrogen increases the extent to which the brain "feminizes", so trans women athletes who are required to be on estrogen especially have no cognitive advantage with regards to hand-eye coordination relative to cis women:

Studies on the cognitive performance effects of [hormone therapy] overwhelmingly support the gender-affirming effect on cognitive tasks that have shown well-established sex differences. Androgens enhance “male-like” characteristics among [trans men] and are associated with decreases in performance on typically male-dominated cognitive tasks among [trans women]. In contrast, longitudinal studies suggest that the opposite is true for hormone manipulations used by males transitioning to female. [Trans women] show a reduction in performance on 3D visuospatial tasks [127, 129] and increased verbal fluency. Relatively few studies have concluded that [hormone therapy] results in no change in verbal or visual spatial performance among those transitioning from one gender to the other [25, 131, 132].

EDIT: the USA Fencing policy requires a minimum of 12 years of testosterone suppression and proof of compliant hormone therapy for trans women participating in domestic competitions.