The right consistently goes with emotion over reason.
The right is belligerently anti-intellectual; they are at best antagonistic to knowledge and to people who have knowledge. They call them elites and intellectuals, they distrust these people who know more than they do, and they resent any need on their part to acquire knowledge and skill in critical thinking.
This is why they like simplistic answers, no matter how wrong they are. Remember the Ebola scare, where the right wing nuts were running around like a character out of Chicken Little claiming the sky was falling? The simplistic - but WRONG - solution they demanded was to ban travel from Africa. This was widely popular among the base on the right, and it was broadly articulated by prominent right wing populist leaders. While it was a solution that medical experts insisted would not KEEP people safer from an epidemic, it made the right FEEL better that they would be safe.
The right consistently goes with emotion over facts and reason.
Obama did not do that, and as a result we had a couple of cases of Ebola, that were well managed, except for that one case in Texas. Swaggering, inept, cheapskate Texas - enough said.
And conservatives were persuaded that if we did not ban that travel, we were all going to die, en masse, with blood gushing from every orifice in an apocalyptic nightmare.
It did not happen. It did not happen because the person in power - President Obama - made his decisions based on knowledge and reason and the advice of medical science experts.
The anti-Muslim and anti-Europe positions of the right, as articulated by right wing leaders and propagandists, FEElS good to emotion driven conservatives. They don't want no stinking information, they don't want to have to think critically, and most of all they don't want the advice of thoughtful and informed experts on the subject.
Which is why Trump and Cruz and the rest can say stupid, irresponsible things on foreign policy and military strategies, and they will be embraced by the right wing nut base.
John Oliver calls it wonderfully.