Short answer: No.
Slightly longer answer: Liberals are more likely to defend conservatives than conservatives defend liberals.
I think there is some truth in that. However, I do think liberals and conservatives alike are both susceptible of accepting a policy based on the paper it's wrapped in. Remember Guantanamo? Where is the outrage from the left? It's largely absent because of who is in office. The left gives Obama an enormous pass. Where was the outrage towards Bush when he was creating entirely new gigantic branches of government and spending money like crazy? It was largely absent because the right gave Bush an enormous pass. People are "fans" of politics and that's an issue. Policy should be what people champion and not politicians. But I digress, I think your slightly longer answer is likely true.
Yes, but I was taking it to mean in general terms and not just in relation to justices.
Even in general terms, though, I think this general trend of liberals supporting the speech rights of conservative individuals more than conservatives supporting the speech rights of liberal individuals holds. Consider all the college campuses where various flavors of right-wing nut get to speak. And then consider the few that trend right-wing, like Liberty "University" and Regent "University", where this happens vastly less often.