Why would the party support them?

Those are the people who do the nost work for the party. People who 'toe the line' are also those who tend not to do the work that gets people elected. People who care enough to think also knock of doors and the other work that gets someone elected. You won't find a thinking person you 100% agree with, but a mostly agree is better than a mostly disagree - and by doing that work you also get to talk to people and perhaps change minds.

For the team? For the influence? There used to be a time when people could work across the aisle.

You can have beliefs, but you also must have heart and a brain to open your world view to other perspectives. This is what being an adult is all about. Not this crap that we see today.

I would suggest that at those times it's when the structure of achieving the same common goal was at stake.

Disagreements on the best day to provide services to the public are still attempting the same common objective.

Disagreements on which people will have their rights removed are not a "let's agree to disagree" sort of thing.