If it was a mistake for the bishops to criticize Democrats on religious freedom and anti-abortion grounds, wouldn't it, for the same reasons, be a mistake for them to criticize Republicans for their health bill? Or is the idea that they need to criticize Republicans to balance things out?

I can't see how the Church would benefit from being too heavily identified with the political Left or the political Right. Either way, the loyalty of its political allies will be fickle and its political adversaries will bear grudges.