With regards to mods chanding the opposite gender anim flag on characters like Lydia. my understanding is if you meet the NPC before your mod is in place, that attribute gets baked into the save game. Have some questions that maybe could help fix that, and also here is what I have tried so far.

First, has anyone really determined this as 100% true or identified where that is in the save file?

One idea I had was try to use the commands to copy stats from one npc to another, but that did not seem to affect animation. Command I used was [ActorRef.]DuplicateNPCStats NPCToCopyFromID

I played around with hex editor a bit, but I'm pretty newbish at that and didn't make much progress. I saw this upage refer to it in NPC file format, so wondering if there is something there that would help. Can't post the link but it is Mod_File_Format/NPC on UESP

Also, one can modify stats using setav, forceav, and modav, but I don't know if that can be used to change this. If it did, would need the actor code, but it's not on any list I can find, however, I do see some "unknown" ones on the Actor_Value_Indices list on UESP

Another idea would be to use hot loading to force a mod to load that changes the anim and then save it to get it into the game. So far though it crashes when I do that. Not sure if it's just my computer though. Maybe someone else can test it out.