Reasonable thing to be confused about. The Federation is post-racial, meaning that on a government level, there is an understanding that race is a social construct with no biological basis in reality, and one that can be done away with. People frequently conflate race, ethnicity, and culture, which while related, are three different concepts.
In the Federal Constitution, under the title of Freedom, you’ll notice a subsection named “Right to Identity.” What does that mean? “Identity” is a big word. In its umbrella, it incorporates 1) sexuality, 2) gender expression, 3) culture. Those are the big ones I can think of, but there’s easily more, and I’m sure there more elements of identity that we’ll discover in the future.
Intaki, Mannar, ethnic Gallente, Jin Mei, Caldari - while people outside of the Federation might call these races for simplicity’s sake, we consider them “interstellar sociocultural categories,” and they’re not frequently used one-on-one, inside member states. In general, within the Federation, people don’t tend to use such big sociocultural categories to define themselves to each other. They use it as a shorthand for people of other empires to understand. I live on a small planet in the middle of nowhere. If I told you my identity, which is related to my member state, profession, and passions, you wouldn’t recognise it. But you will understand “ethnic Gallente.”
When you talk to someone who lives in the same city as you, you tell them what neighbourhood you live in. When you talk to someone who lives in the same country as you, you tell them what city you live in. When you talk to someone from a different country, you tell them what country you’re from. It’s an approximation a little like that. When someone says they are “ethnic Gallente,” they’re not wrong, but they’re not being as precise as they could be.
So, yeah. I showed up one day, from somewhere else. I never felt quite right in the culture I was born. I don’t think that culture much liked me either, given everything its members did to me. I liked some things associated with the ethnic Gallente umbrella. So I moved to Gallentia. I explored heritage sites, I listened to people who had been identifying as ethnic Gallente for far longer than I, I read the histories. I sung our songs. I’ve done more that would make this post go on far longer than it needs. It felt right - it felt good. It made a sense to me that nothing else had at that point. I’ve been ethnic Gallente for, oh, nearing fifteen years, and I don’t regret it. I don’t know if I’ll always feel this way, but even if I don’t, it’s not like I’ll be punished if I change my mind. I’m pretty sure this is who I am, though.
I talked about the ethnic Gallente case here, if I’m not making much sense. It’s hard to explain to someone who hasn’t lived it, I think.
Now, if you mean how does that actually work as far as how well it actually works in practice, that’s a mixed bag. Some identities took to it better than others. The ethnic Gallente, Caldari, and Intaki didn’t have overmuch in the way of racial strife when the Federation started becoming post-racial - they had different metrics by which they defined themselves and each other, things they considered far more important. The ethnic Gallente had already ■■■■■■ their ancestral history into a muddy puddle, anyway. Even back at the foundation of the Federation, an average ethnic Gallente frequently had more ancestors from planets other than Gallentia than they did on Gallentia, and the individual nations of Gallentia mixed until skin colour/ancestry meant absolutely nothing. (Immigration didn’t help matters. Gallentia has bigger populations of people on it who immigrated there sometime in their ancestoral history than people who don’t.)
Then you have the Mannar and the Jin-Mei. The Mannar definitely subjugated all their neighbours on their planet for generations upon generations, before joining the Federation, but somehow that never comes up. Did the pain of smaller identities from Mannar VIII get erased when the Federation became post-racial? I know the names of many that still exist, but I can’t imagine it helped their case any. The Jin-Mei literally created ethnostates on Tei-Su through genocide of all non-Jin-Mei races before they met the Federation, but it seems like everyone’s forgotten that too. And in newly-joined member states, post-racialism takes a while to seep in, so you’ll see people in places like Lirsautton still informally recognise race as a system, although that’s literally unconstitutional.
I think it might make a little more sense if you consider it with respect to the difference between race and tribe in the Republic. The Minmatar who’ve immigrated here seem to put an emphasis more on clan and tribe membership than race, anyway.