I dunno, literal genetic modification (even if temporary) as an approved starfleet project vs "I happen to be from a group that practiced genetic modification"=LIFE IN JAIL WITH NO OUTSIDE CONTACT happening in just 2-3 episodes seems a bit of a stretch.
And yes, I see little difference between "we genetically modify ourselves and our children are just as culpable for that decision" and "I am the child of a human and a genetically superior race with enhanced capabilities over a normal human" at the 50,000 level. What, exactly, is the concern over genetic manipulation that would separate an illyrian from Spock?
Well, first of all, it wasn't Spock's choice to be mixed race, but even so, being a child of parents of two races is a natural thing. Unless you're like, you know, a space racist or something. Not saying that you are but what you're arguing here has the same connotations as racial segregation of mixed-race children, so consider that at least.
And no, a plastic surgery that's meant to conceal your identity is nowhere near being a genetically engineered superhuman with superior strength and intellect. Nowhere in this franchise's long history was this ever a sticking point because in the older shows, the implications was always that it was some form of advanced plastic surgery. Usually it was just called a "procedure" or something along those lines, and you would usually see characters entering sickbay in one scene and then in the next one they would just appear with those fake movie props glued to their faces. But otherwise they would always retain their natural physiology - they still bled their own blood, they had the same internal organs, etc.
Strange New Worlds is pretty much the first Star Trek show that tried to explain how exactly these facial modifications are done but this DNA-rewriting hypo spray idea does sound kinda stupid tbh and I wasn't a big fan of that explanation. I think they kinda dropped the ball on that part and I get how you could interpret that as a plot hole. Regardless, it's not such a big deal. It's just a TV show anyway. It's not like they suddenly turned into Khan just because they got a shot that made their faces turn into a potato for a few seconds.