This reminds me of the wedding cake maker several years ago, and if he should be forced to make a cake for a gay wedding which he did not want to claiming religious beliefs. This thread seems to have the opposite view in that the religious people are forcing themselves on the other side.
That's actually a misunderstanding of the case(s) on your part. It's a common misunderstanding but still a misunderstanding. Or concluding that it relates to this demonstrates a lack of understanding of the case(s), rather.
If the wedding cake maker in question had refused to sell any kind of cake at all to the person because they were gay or black or w/e, they would have lost that case(s) in both the UK and the US, because they'd be just straightforwardly violating the law.
The specific issue was, in both the UK and US cases, that they were being asked to create a CUSTOM-DESIGNED wedding cake for a gay couple who were getting married, and that's
different, from a legal perspective, to just "doing business with", or selling something to someone of a protected class. Maybe it shouldn't be, but it is (and to be honest, I think it should be, otherwise you could force artists to draw homophobic pictures etc).
As such it was a
free speech case, because of the CUSTOM-DESIGN of the cake, not a simple case about goods and services. The determination, in both the somewhat homophobic region of the US this happened in, and in the UK, one of the most gay-friendly countries in the world (just we have an insanely transphobic media and politician class right now, that's a long story, but most of it is down to "JK Rowling sucks real bad and is real rich and the media worships her as a dark god"). Like, if I went to a cake maker and said "Yo, I need a cake which says Call of Duty Sux, Battlefield Rulez", they could say "Nah mate, I disagree, not making that", and that applies even with protected classes, because it's a free speech thing essentially.
Here's an okay Wikipedia article on the UK case:
Lee v Ashers Baking Company Ltd and others - Wikipedia
EDIT - Note particularly that Peter Tatchell, one of the bravest and strongest gay rights activists in recent British history agreed, ultimately, that no-one should be able to be forced to write/say something they disagreed with, because obviously this is a double-edged sword, and it's best that no-one gets cut!
Absolutely none of that is relevant to a payment processor, because they're not making something custom, they're not expressing free speech at all, by generically enforcing the bigotry of weird Australians who they are inexplicably afeared of. They are supposed to just process payments, not to try and enforce foreign morality on perfectly legal businesses.