This is getting into issues well beyond this thread, but I don't believe that the two concepts are incompatible. If, for instance, the majority voted to restrict the participation of certain groups in the political process, that would be an issue worthy of supreme court review because the political process could not adequately resolve the issue (because the offended group has been barred from participating in the process). What I said before was perhaps inartful. Maybe I should have said that the Court can become involved essentially to ensure fair play in the political process, but only in those circumstances in which the political process couldn't adequately resolve the problem itself. For instance, if a state legislature votes to make a public school male-only, I would contend that the courts would have no business in reviewing that action because the political process still works and the public is free to take action to make a change in the legislature, if necessary. If the same legislature voted to deny the franchise to women, that would be an issue for the courts because that affects the fair play of the political process. I think this approach is one of the few ways that a court can take cases that don't veer into the realm of "judicial activism." It becomes far too difficult in the former category of cases to make decisions without injecting personal political bias, and I think that is a problem with the judiciary.
“I don’t believe that the two concepts are incompatible”
Exactly so. “Republic” literally means a government by the people, and “democracy” literally means rule by the people. Everyone gets all in a huff about the distinction between the two, but really it’s all about conotations. Remember, commies use the term republic all the time. Heck, Rome under the rule of the Senate called itself a republic. To the Founders, “democracy” meant “majority rule,” whereas “republic” probably meant some form of “mixed government” (in the Aristotlean sense). The words need not mean as much to us. In fact, I’d argue that in general usage they mean pretty much the same thing. That’s one reason why I constantly hear our government refered to as a “democratic republic.”