Part of being an American is picking a team and sticking with it. If you don't like something about it, change it. I understand there are times when "the party leaves you", but it would be a really, really big coincidence if those times just happen to be when it is politically expedient.
Alabama Democrats give Republicans supermajority
I hope these new Republicans lose their next election so the ethos is understood to be loyal to your political party. Parties matter because of history, discipline, and structure. We have too large a country to have chaos in our political institutions. Everything can't be enshrined in the Constitution(s) or the law, so we need political parties to form and work together. Politics is war without the bloodshed. That means you just can't cross the aisle because your side loss, and it's going to be tough. If these representatives really thought their constituents would be better served with Republican members then they should resign and run again as Republicans or come up with some novel ideas.