Somehow the (conservative) Evangelical churches managed to live through the tumultuous 1960s and 70s without a mass exodus of followers and an infiltration of radical social leftists.  Why should it be a wonder or a ill advised for those in the Church - who have watched their Church be simultaneously attacked, changed, and liberalized while the leftist radicals attacked US social institutions - to align with a religion that retained its conservative social morality that was previously accepted by all Catholics?

It's classic CONSERVatism against relentless attacks over the last 50 years against the Church. 

I think there is fear in the progressives, worried that this alliance of Church and Evangelicalism will lead to the undoing of 50 years of destruction of American culture and the Church.