people who are part of the LGBTQIA+ community already have those legal and civil liberties with regards to insurance, beneficiaries, etc., so then as you say, there should be no more fighting for those rights, since they've already been granted or included.
If the movement is about fighting for injustice, then they should fight against all injustice against everyone, such as babies and white people, rather than just a very particular slice of injustice for a particular group of people "of color".