I was unable to find an adequate term like "state engagement/involvement", this was the reason of my "etc."...:)
"I haven't yet made up my mind on the significance of the last part." Just like me.
"wasn't the majority 'there' already?]"
Definitely yes. But this majority is growing. - And let me put a smiley here :) -
Much depends on the Hungarian Left. I mean those people who are not part of the terminally ill "left-liberal" establishment. The situation is "open".