Did the filmmakers of Zootopia have a "gay agenda"?

No agenda, or perhaps just an open one.

At the end Judy reflects that Zootopia is not a dream place, it's more complex than that.

I thought Zootopia was this perfect place. Where everyone got along and anyone could be anything. Turns out, real life's a little bit more complicated... than a slogan on a bumper sticker. Real life is messy. We all have limitations. We all make mistakes. Which means, hey, glass half-full, we all have a lot in common. And the more we try to understand one another... the more exceptional each of us will be. But we have to try.

Many references to the movie point out in a rather explicit way that biology doesn't define how you act, or if you're a good or bad person. In that sense one can understand several readings:

• Against Lombroso's XIX century criminology that dictated that one could know a criminal profile according to physical appearance, or head-shape. This type of thought was still mentioned as phrenology in a not so old movie: Men at work (1990).
• Against the idea that there are only two biological sexes. Gender is defined and built socially, hence not dependent on biology. This interpretation of sexuality may allow more ambiguity and openness such as suggested in another answer in this SE about the relationship between Judy and Nick.
• Perhaps a black agenda is present too in Zootopia. When Judy arrives to the ZPD station headquarters they say she is such a cute bunny, and she refrains and responds that only one bunny can call another that way.

2 additional notes.

1. On sex & biology an interest view is presented in a movie that refers to a person that is born transgender (hermaphrodite): XXY (2007). It's not documentary but based on a real life person.

2. There should not need be any connection between:

   • promoting "homosexuality" and "non-binary" genders; and
   • conspiracy theories

Those people fearing a gay agenda see the movie "promoting" certain things, peoples, and behaviours; I see it more as "showing a modern world", a nowadays city where you have the rich, the poor, the weird, the gay and so on. But as we know, some people don't like to see some of "those" around, and see a purpose of enfatization where there is none. The movies promotes acceptance of diversity, but they made a point of not making direct translations of racial stereotypes (Ex: Mr.Manchas sounds like Sanchez, but hasn't hispanic stereotypical traits; he's a black panther but has no black traits).

I didn't see any mention of LGBTQ+ persons in Zootopia, so no it doesn't have a "gay" agenda. More like an inclusive, modernist all-are-welcome agenda which could annoy people who are less open.