So I’m a male, fertile so far as I know. Suppose I walked into the county courthouse, hand in hand with my sexy sister and asked for a marriage license. Naturally, the clerk would say “GTFO you disgusting freaks. You’s brother and sister and we don’t need no more incest babies in this county.” If I came back the next day with my beautiful brother, the clerk, seeing that our union would produce no natural offspring, agrees that love is love and we just need to sign and notarize these forms.
Party affiliation as listed on voter registration isn’t a loyalty oath either. It’s just a way of asking which primaries you want to vote in. You might as well pick a party with relevant primaries in your area whether you agree with their platform or not.
(Voter registration is public information and may affect which candidates and PACs send you mail.)