This “debate” is, frankly, pretty dumb.
Was it silly for Warren to put down that she was part Native American all those years ago? Sure, of course. Would it be extra silly for her to bring it up now? Yeah, but as far as I know she only talks about it when people attack her about it. It should be irrelevant at this point.
As for how I’d be reacting if a Republican was in the same position, it depends a bit. If they’re someone who’s serially dishonest like Trump, of course I’d be a lot more skeptical. If they were exactly the same as Warren I promise I truly wouldn’t care (not like there’s anyway to convince warb once he’s set his mind on something). The fact that she doesn’t look Native American shouldn’t matter, it’s honestly pretty rude and ignorant to think that someone of specific heritage needs to look a specific way.