I’m used to the idea that, in or out of executive office, a party has a leader whose job it is to keep the party as together as possible, and (particularly in the aftermath of defeat) to come up with both an over-arching message/narrative and supporting policies that would form the basis of the formal manifesto/platform for the next election. In the US does that formal responsibility live with the Chair of the relevant National Committee or the leaders in Congress (and which has priority?)
It would be normal to expect a party, if it’s to be effective, to be seen to be united around core principles and policies. Maverick candidates and MPs are allowed a certain amount of latitude, but if it’s in the manifesto and they oppose it, there’ll be trouble.
Mind you, in our case, abortion would be one of the few “conscience” issues that no party would dream of putting in its manifesto, leaving it up to the judgement of individual legislators, nor, come to that, is there any difference in the attitudes of any of the serious political parties to gun control or the principle of universal provision of medical care - but that’s the UK for you.