Give Me a Break: who said that you cannot use religion when making a choice for a person running. you can usxe any litmus test you choose as a free thinking person in america. whether the rules of church and state exist in the way most people think is another issue, but it definitely does not apply to stopping a person from making a choice. morally it is no problem, as non jews make these decisions as well, whether it was kennedy telling people his catholicism wouldnt mean much as president, or that mitt romney was attacked as a mormon by some evangelicals. jews are by far not the only ones who use religion and support for other countries as a litmus test for nominees.
besides that, there are other things as well, nothing to do with religion, that jews, especiallly orthodox ones, tend to associate themselves nationally with republicans (not to mixc up locally supporting democrats). things like vouchers, lower taxes, marriage and children tax deductions, and more all appeal to orthodox jews as well. yes israel is a big one, but there are others as well.