Now tomorrow has come, and you ended up as one of the branches. How much do you care about the others you did not end up on?

In the case of MWI physics, I don't care about the other copies at all, because they cannot interact with me or my universe in any way whatsoever. That is not true for other copies of myself I may make by uploading or other mechanisms. An upload will do the same things that I would do, will have the same goals I have, and will in all probability do things that I would approve of, things which affect the universe in a way that I would probably approve of. None of that is true for an MWI copy.