First of all, the shape of their body aswell as the fact that they got lipstick (something that so far only female animatronics had) makes atleast their design female like. Appearance has nothing to do with gender though, it just shows that William wanted Funtime Foxy to look female, regardless of what gender Afton "planned" Foxy to have, if he even thought about that at all.

Now we can start with the first time someone used pronouns for Funtime Foxy.

In Night 2 of Sister Location, the "Angsty Teen" voice option of Hand Unit refers to Funtime Foxy as "he" (Look at the 2nd Image for his full voiceline).

In Night 3 of Sister Location, Hand Unit (now back to his default, adult voice option due to the other one breaking) refers to Funtime Foxy as a "she" 2 times (Look at the 3rd and 4th Image for his full voicelines).

In the non-canon Custom Night of Sister Location (only the events are non-canon, the characters, the office and everything revealed through voicelines aswell as the cutscenes are canon), Funtime Foxy's description refers to them as a "he" (5th Image) but he is also part of the "Girls Night" challenge (6th Image).

In Ultimate Custom Night, Funtime Foxy's description once again refers to them as a "he" and he once again is part of a challenge only featuring females, this time being "Ladies Night 3" (7th Image).

Since Fredbear is the one who is in control of UCN it is possible that he is the one who made the descriptions and challenges, though the menu is most likely non-canon.

Funtime Foxy only talked in UCN so far. They use a male voice but since they got the ability to mimic the voices of parents, as seen on their blueprint (8th Image), it's possible that this is not Funtime Foxy's true voice and instead just a voice they chose to use, possibly because they like that voice. If that's the case, Funtime Foxy would most likely be female-to-male, because someone who sees themselves as a male, naturally wants to sound male aswell.

In "Toy Chica: The Highschool Years" one of the 2 animes in UCN, Funtime Foxy appears as one of the students that get lured and killed by Toy Chica who is a metaphor for William Afton. In Episode 4 (9th Image) aswell as the first few lines of Episode 5, after Funtime Foxy has been killed (10th Image), Toy Chica refers to him as a "he" and calls him a "guy". This might not be relevant though since that entire anime is just a metaphor for William abducting the missing children to harvest presumably their remnant. It's likely that some characters genders might not be portrayed accurately since both The Puppet and Funtime Foxy have a male appearance (excluding their make-up) specifically their male looking body. It's possible that Toy Chica still used their correct pronouns though since both Funtime Foxy and The Puppet are refered to as "he" in their descriptions.

In Help Wanted, Hand Unit (default voice option) refers to Funtime Foxy once again as a "he" (11th Image) due to his voiceline being reused except for the words "Unlike Ballora". Oddly enough the Hardmode variant of Funtime Foxy's level in which they get replaced by Lolbit is still called "Funtime Foxy" despite the fact that Lolbit now serves as the level's main antagonist.

In Help Wanted 2, Funtime Foxy makes their last known appearance so far, though only as a videogame character as the real Funtime Foxy got destroyed in the fire at the end of Freddy Fazbear's Pizzeria Simulator, being merged with Ballora and Funtime Freddy, now called Molten Freddy. The instructions for the level "Funtime Gang" featuring them, refers to Funtime Foxy as a "they" (1st Image), which basically confirmed Funtime Foxy to be trans. Obviosly anyone can use any pronouns, no matter what gender they identify with but "they" is most commonly used by transgender individuals and due to Steelwool introducing gay animatronics to the Fnaf universe in Ruin it's likely that they now wanted to bring another letter of LGBTQ into the franchise.

Additionally the Freddy Files call Funtime Foxy a "he" aswell, though it's unknown if the informations of this book can be trusted due to small mistakes.

Now I summarize what I think is going on:

Funtime Foxy was built as a female animatronic by William (female design).

Funtime Foxy identifies as a male though (male voice and the fact that different pronouns are being used for them in the first place).

Hand Unit's default voice option, which seems to represent an adult, is programmed to call anyone by their gender assigned at birth, something that real adults are more likely to do than teens (intentional or not) and continues to call Funtime Foxy a "she".

His Angsty Teen voice option however, is programmed to respect the gender identities of others and calls them a "he".

They appear in "Girls Night" and "Ladies Night 3" due to their female body (similar to how irl trans people are forced to use the incorrect restrooms if they haven't done surgery yet) though the custom nights descriptions refer to them as a "he" to respect their gender identity.

The anime "Toy Chica: The Highschool Years" could possibly be an official anime by Fazbear Entertainment, which at the same time is there to give us some lore similar to the "Freddy & Friends: On Tour" cartoon. If that's the case then Fazbear Entertainment not only respects Funtime Foxy's gender identity but also wants to present him the way they want to look like in any future commercial material.

In order for the events to stay unchanged the Devs of Help Wanted (the in-universe Devs) kept Hand Unit's dialouge unchanged, meaning that he still calls Funtime Foxy a "she". If there would be a text or a different character talking about Funtime Foxy it would probably use their correct pronouns, though unfortunately Funtime Foxy only plays a small role in the game and thus isn't mentioned that often.

Later in Help Wanted 2 the Devs of that game (in-universe) obviosly use Funtime Foxy's correct pronouns once again. The reason why it's "they" instead of "he" now is most likely because Steelwool wanted to let us know Funtime Foxy's gender, so that not only trans people can have a sort of "idol" in the Fnaf franchise but also to finally put an end to the whole Funtime Foxy gender debate. I doubt that they'll change anything about Mangle though since Scott already stopped the war by making Mangle's gender "yes".

Alright hope you enjoyed my "theory". Also anyone who wants to insult me or the lgbtq community because of this post should just leave me alone because I'll otherwise make fun of your stupid attempts of trying to hurt people. Like seriously, last time there were some hate messages which were just pathetic lol