I think the issue is subtler. The vote arithmetic goes both ways: under a different cultural conditioning voters would desert a politician with Islamic sympathies. The real culprit is the indoctrination into the anti-nationalistic mentality, where everybody is afraid to love his own nation, civilization, and religion.
Oh, no doubt. The Left has done a great job stomping Christianity and patriotism out of society these past sixty years. Yet people will not believe in nothing. Islam is a statist creed, which the Left encourages to fill the void.