The truly good reason not to be comfortable with people's ideological statements is that they are tied to nothing. Jeb Bush said only Christian refugees should be allowed into the US. When asked how to know if someone is Christian he basically said, just ask them, we'll know. How many people will goof up and admit that they are ISIS sympathizers and only realize their mistake later upon reflection after their application is denied?
The only way to prevent anybody objectionable from entering the country is to deny entry to everybody. But, since the husband in the San Bernardino shootings was a natural born citizen from Chicago, a hotbed of Democratic Party activism, lawlessness and insurrection in the US, we'll have to flush out undesirable citizens across the entire country, too. If some on the right have their way, that could amount to about half of the adult population being escorted to the nearest doorway built into the new wall. In a twist on a favorite Republican meme, first they came for your voting records, then for your donation history, then for ...