I think it depends on the political climate and context.

In possibly another day and age -- in the US where I am or in my motherland -- I wouldn't have perhaps cared as much if the therapist turned out to hold political views opposite to my own (left).

However, in the present day (both in the US and back home), leaving aside all moral issues, I'd seriously question the therapist's intelligence / basic cognitive ability if they turned out to have political views opposite to my own.

And yes, I would quit -- I couldn't possibly take the therapist seriously in any way whatsoever if that turned out to be the case and so, therapy would go for a toss, anyhow.

At other times, eh, I wouldn't have particularly cared and I might even have enjoyed sorta kinda debating stuff.