The birth certificate being a contract is actually a pretty core SovCit belief that almost all of them will have in some form.
The idea is that your birth certificate is the thing that officially registers 'you' to the... basically they think that the government is actually fake and has been a corporation, after a totally historically covered up total bankruptcy of the US that ended with the entire country effectively being placed into recievership... though when and how this event occured varies: either after the Civil War, or when the Income Tax or Federal Reserve became a thing, or the Great Depression...
Either way, yeah, the birth certificate is what they believe registers you as an entity that is subject to laws, taxes, debt, etc, which all stems from the 'fake USA corporation' idea, so the bankrupt US can keep paying off all of the debt it owes to this 'psuedo US government but actually its a recivership legal entity' thing... and then almost all the rest of their nonsense legal theories revolve around 'weird legal tricks' that circumvent all 'fake' laws passed by the 'fake USA corporation' and go directly to pre-existing laws / legal norms from before the 'fake US government' took over.