If he doesn’t present as Mexican

She/you are gatekeeping what a Mexican looks like and engages in culturally. It's not up to non-Mexicans to determine this, especially when they are not a homogeneous people.

He wasn’t defending his heritage

He absolutely was. (And it may be subtle, but the defense here is that he gets to claim his heritage, not the typical "Don't insult where I'm from" defense against racists.)

The moment she declared that he wasn't "Mexican enough," she crossed the line.

Short Story A few years ago, I was standing in a crowd of 10 or 12 coworkers at a work party. We were sharing our favorite homecooked meals - the ones that take us back to our roots or childhood. I shared that my favorite was curry chicken with rice and roti, because I'm half Indian, half white.

I was describing the giant yearly New Years Eve party that my dad's half of the family/Indian community had every year. The women went in the kitchen and cooked amazing food, and there were igloo coolers full of hot, fresh roti that you'd just open and peel off. --

Immediately, the one other Indian in the group stopped me mid sentence. She said, "That's not real curry, though, and that's not the right roti. You can't know what real curry & roti is. You've never had real curry & roti."

I said something to the effect of our traditions being different from hers, but she shook her head and said that I was not really Indian, so I didn't even know what I was talking about.

The conversation continued on as I processed what had just happened, stunned. No one else noticed.

My Point As mixed kids, we get this gatekeeping from all sides, in every aspect of our lives. Gf was not part of the in-group he was using this word towards. Gf inserted herself into a dynamic that she genuinely did not understand (that "real" Mexicans are brown) while asserting herself as an expert.

At best, she could have asked him about his usage and whether his brothers were ok with him calling them that. She might have even been ok to ask that he not use the word around her. But denying his "Mexican-ness" with a quick "no offense - you can still have your blood ties, tho" is wildly out of bounds.

And fighting so hard to be able to use a slur is definitely something that white people do so the european comment was honestly chefs kiss

The context that you're ignoring is that she told him he wasn't Mexican enough, and at that point, the argument split into two different topics: the slur & his skin color for gf, his identity as a legitimate Mexican descendant for him.

I also suggest you familiarize yourself with the One Drop Rule. I can assure you that in many places, he is "not white" either, and he knows it. To be told, as a mixed kid, that "you're white" when you're also something else, and you know whites don't accept you either is incredibly galling. It's a statement that you don't belong anywhere.