What is the “right” at issue here? It’s not the right to free speech, since the self-financed candidate still can speak as much as he likes. It’s the “right” to have the loudest voice if you have the most money, to drown out every other voice.
Which isn’t a right at all. It’s a privilege: the privilege of those with money to bend the political system to their will, to have the biggest megaphone, to make sure that their money gives them the ability to put a thumb on the electoral scale.
Conservatives favor those with money, so expect this one to be a 5-4 decision one way or the other with the 4 conservatives on the Court voting as a bloc.