The selection of the new Supreme Court Justice, particularly in these times, is arguably the most important appointment in America's history. He (it certainly won't be a female) will be making decisions that could set America back decades, particularly on women's right to choose what they do with their own bodies. For this reason alone, Democrats should oppose any right-wing nominee. 
At least in Canada, even the most right-wing politicians have agreed that the issue on abortion is settled. 
Religious beliefs should not dictate politics. The separation of church and state is fundamental to democracy.