On the gender/sexual stuff I think you're right. On the rest - no. JPII had a genuine commitment to religious tolerance, democracy, and reaching out to people of different views (as long as they weren't part of the Catholic hierarchy broadly understood - no place for democracy there). He began reaching out to secular leftists disenchanted with communism early on in his period as archbishop, on the grounds that regardless of their theological differences, they shared many broader social and political values. This was a rather controversial policy within the Polish Church whose conservative wing doesn't really see any difference between a liberal (neo or not), social democrat, or communist - all heirs to the French Revolution and proponents of modernity.

I also think he was more left wing in his socio-economic views, though that's harder to be certain of. The Church offers a dual critique of capitalism - one has to do with the evils of individualism and liberalism, the other with economic inequality. Both Popes speak of both aspects, but JPII tended to place more emphasis on the latter than Benedict, particularly post '89.