Seriously, I don't care so about the label. It is what you do and how you vote that I care about. I am a registered independent and I vote for the best person (whatever party they represent) and not just because they belong to one party or another. JMHO
So you would have voted for her (if you lived in that district) in the general election because it was her against a Democratic? Or maybe you'd have voted for the Democrat depending on the particular positions on particular issues? Or you'd have voted for some independent, libertarian, or other candidate?
One of the "issues" in this case for me is that when she ran as a (Republican) party member she got at least some money from the (Republican) party to run her campaign, which in this case, her election being only four months ago means that Republican Party members who gave money to the Republican party in general helped fund the election of a Democrat. I'm pretty sure that most of those donors didn't want to aid and abet the election of a Democrat, yet for the next nearly two years that's exactly what they paid for. Who knows, maybe the don't care, since I read that she was "primaried" by a more "conservative" candidate but she won handily... I wonder how much Republican party money she spent (as the "incumbent") in the primary compared to the challenger (I'd guess they got zero from the party). Maybe the Republican party itself is at least partially to blame as it's up to them to vet the candidates, and I guess if they believe they can only win by running a RINO, who is really a Democrat, and give that person money to campaign, that that's their business. Who knows, maybe the Democratic party gave her money as well? Wouldn't surprise me, especially in the primary.
I asked Fukumoto in an email if she'd still be a "Republican" if Clinton had won the election, but she hasn't responded (yet?).