You can be a trans ally by accepting that some people are trans and respecting their right to have that choice. That's all it means. It doesn't mean you accept or want gender stereotypes to exist, but the fact is that sadly, they do, and some people are impacted by them and have desires/ needs to be trans. This view is not in opposition with being a feminist and working towards a better and more equal society. It is simply a realist view that we are not there yet and in the meantime, people will make choices that are right for them.
But stating your own pronouns is declaring that you have a gender identity. It might not be that that's what OP's person is saying (as we don't know her specific reasons), but unless she has simply done it to look cool, if you take her at face value, she is saying that she believes in gender identity ideology, similar to how walking around wearing a crucifix would lead people to assume you're a Christian (even if the truth is that it's a family heirloom or you just think it goes with your outfit or whatever).
I agree with you that some people think that stating their own pronouns means "I accept that some people are trans and I respect their right to make that choice", and obviously feminism isn't incompatible with that view, which is just basic human decency to accept that other people have different beliefs and should be free to express them.
However, stating one's own pronouns goes one step further than merely supporting people in their belief that they are trans as it indicates that the person accepts that belief as real to them too. Which is fine; totally their choice to believe what they like, but believing in the existence of one's own inner sense of gender identity is very different from merely supporting trans people.
I would also argue from my own experience as an autistic lesbian that non-trans people stating their pronouns doesn't merely support existing trans people but actually creates new trans people and exacerbates gender distress, as the rest of us who are trying to work out what gender means to us (including children and young people, gay people, GNC people, neurodivergent people, and so on) often interpret a non-trans person stating their pronouns as saying "yep, I too have an inner sense of gender that is so evident to me that I'm sufficiently confident to declare this fact to the world". And so the rest of us who are wondering what on Earth everyone else is even talking about what they say 'inner gender' start to worry and think we must therefore be trans because all these non-trans people can feel their gender identity too and we can't.