What will be the social ramification
What will be the international reaction
How will it affect Britain as a whole?
Social ramifications in Britain during the 70's and 80's? None at all. It would just never be spoken about. Not even by the Red Tops. Ever. It would be taboo to even joke about it. I doubt even the "Radical left" comedians like Alexi Sayle, Ben Elton or Harry Enfield would joke about it, certainly not on the BBC. You
might, at most, get a "Queen Charles" joke on a late night Channel 4 live show, But very, very rarely.
There's nothing like the "establishment" closing ranks around the Royals. So the effect would be minimal. Probably a quiet act of Parliament to allow Prince Charles to abdicate his position in the line of Succession.
Not sure about international reactions though.
Would Charles "come out"? I think if he did, it would likely be in the late 90's, in the Blair years as part of "Cool Britannia". I doubt there'd be an announcement, I think the taboo would gently dissolve until his sexuality was a matter of open discussion.
At this point, I could see Marriage Equality passing about 10 years earlier than OTL, but that's about it. If it did come to a defining moment, it would probably be a very small piece in the London Gazette that former Royal Navy Commander Arthur Windsor married his long term companion [add name here] at a registry office near [Cornish town].
I don't think you'd get a "Royal Wedding" out of it. Questions about a later generation coming out might be better suited for Pol Chat.