MLK, we have already discussed the issue of shaking hands with women (which also applies in the business world). BTW, when Rebbetzin Jungreis met with Bush II he was told in advance not to extend his hand and there was no problem. For a candidate there would probably be elss than an issue becuaue he shakes so many hands that it’s most likely a nuisance for him.
As for anti-Semitism, that is a problem although today religion is not an issue, Nobody, for example, would consider asking a Catholic if he would let the Pope run the country as they asked JFK. There are Jews on every other level of government including SCOTUS (BTW, Stephen Wise opposed Felix Frankfurter’s nomination because of this issue and it did not pan out even though anti-Semitism was rampant in America at the time). Whatever one thinks of him Obama proved that there are no longer bars to minorities. Moreover, Jews have been advisors to Presidents from both parties with no repercussions (unlike when the new Deal weas called the “Jew Deal”). Of course, being the power behind the throne has certain advantages. How many people know that Ted Cruz’ senior adviser and deputy chief of staff for strategy is a frum Jew named Nick Muzin? Yet he certainly exerts a great deal of influence, possibly more than if he were in the limelight.