Saw them in Philadelphia in '66 and in Auburn, Alabama in '68 -- with Chuck Berry as an opener! -- and they were always anti-establishment. It's just that it isn't cute any more when you are 'way, 'way old enough to know better.
I have the feeling that somewhere in time I remember reading that Jagger was personally very conservative. He was a Tory. Of course, in my dotage I may have him confused with Rod Stewart who (if I remember correctly), I was madly in love with. :*)