From what I gather, US Non-profits have a right to free speech. That’s how political PACs and other orgs can out out their own campaign messages/ads. US non-profits are required to be against prostitution by law to be eligible for i1st amndmt. Open Society has not been against prostitution and claim they have to be neutral due to some of the locations they work in. Hence Open Society has just lost their 1st amendment rights in the US.
I don’t know if it affects their ability to pump money into candidates.
Nope. There's a 2013 Supreme Court decision specifically upholding their 1st Amendment rights in the US.
This case is about their foreign affiliates.