As another Catholic commenter said, we owe Christian charity to all other human beings, including those affected by gender dysphoria. However, charity doesn't mean being "nice" or "accommodating," but it does require respecting the dignity of the human person. One way to respect that dignity is by not encouraging or condoning disordered behaviors or beliefs. I wouldn't offer a recovering alcoholic a drink, even if it was really great stuff.
That leads to another pragmatic matter. No matter what disordered beliefs or behaviors a person has (and I have my own share), we should want to help that person come to a rightly ordered place. There's really no one size fits all approach to that.
You know you can do this with trans people too. Or do they not have names?
These are all reasonable questions. I'll answer as best as I can, but please understand that I'm not any kind of formal authority.
> If you cannot use requested pronouns, does your religion also ban you from using nicknames? Is it okay for you to be called User23?
I don't know of any Catholic doctrine that says people can't use pseudonyms, nicknames, or even change their name altogether.
> Is it okay to say someone's cat is cute even if you don't really care for cats? What do you do if your partner asks if they look good or bad in something?
Is it a lie, which is to say a falsehood told with the intent to deceive? Then yes it's wrong. Wouldn't you want to be told the truth if you in fact looked bad? Wouldn't you want to know that when you're told that you look good that you really do?
Personally, supposing I didn't think the cat was cute, I wouldn't say I thought it was. I would most likely treat it as a good opportunity to say nothing on the subject. Some theologians put forth a doctrine of "mental reservation"[1] which somehow makes lying OK, but I have to admit I'm not capable of the necessary mental gymnastics in any but the most clear cut cases.
[1] https://www.newadvent.org/cathen/10195b.htm