Rights begin simply as things sentient empathetic and sympathetic beings understand they want, and therefore other people probably want, and so they as a collective work to guarantee these Deserves to each other (society) because they think that is right. “Rights” are not given by some cosmic magic, but by people as a society.
Some groups of individuals have had those Rights or Deserves specially infringed on because of their membership in that group. The logical conclusion from recognizing such marginalization is of course to target that group for advocacy. Such advocacy for that group is not equivalent to being against the group that already has the Deserves/Rights. Advocacy isn’t a zero-sum game.
Additionally, recognizing that group for advocacy is not the same type of discriminatory group-making as those who initially targeted those people for discrimination.
Trans rights are when you recognize that trans people shouldn’t be excluded from Rights as undeserving because they are trans, and you therefore seek to raise them back to equality through advocacy because you feel it is right.
Feminism identifies where women aren’t accorded what you feel are their Deserves that men are accorded, and you therefore seek to get them those Deserves through advocacy.
And so on down the list for gay rights, black rights, Muslim rights, Atheist rights, and the rest. Advocacy for one of these groups cannot reasonably be interpreted as not being for everyone’s rights. Some crazies may try to tear down others while gaining rights for themselves, but mere advocacy doesn’t define you into that group like the people who knee-jerk with “all lives matter!!” or those who were triggered by the Gillette commercial seem to believe.
Some people feel it is best to look at things as “natural rights.” I can see where they are coming from; the sentience and capacity for empathy and the desire for food, water, and good treatment are all things we naturally evolved. The problem is that, for example, it would be “natural” for a lion to hunt me down and eat me if I lived near one. What was natural in that case was good for the lion, but bad for me. As a result, I don’t think what is “natural” is necessarily the best argument.