(with due credit to Rand)
Basically, people don't take all that kindly to alien contexts and preferences being imposed on them. In the case of religion the alien cognitive context is one or more religions one doesn't share, differentiated in content by items of faith ultimately inscrutable by earthly reason. So two people get into a heated debate over which of their respective revealed dogmas is the more reliable and truth-reaching. But given that these rationally inscrutible items become the very point of contention, a matter of context not shared by the two participants, the participants are left with asserting the truth and authority of their position over and against the preconditions for rational assent by the other - an assertion or imposition of epistemic ground against the recipient's wishes, in effect. This is because the healthy rational and skeptical aspects of personality naturally kick in when it's the other's dogma being asserted as authoritative truth over and against one's own dogma. In any case, any differences of opinion could not in principle be solved rationally from that point forward, and that tends to rightly irritate people who are otherwise calm, cool and and collected thinkers. They don't have time for inscrutibles. Etc.
In the case of politics, it's much easier and simpler to explain: people don't take kindly to having others' preferences imposed on them by force, and that's what politics in this day and age is all about. Since when does the vote give you the right to dispose of my life? Actually, this sort of question can only be asked, without irony, by libertarians. In fact, the libertarian will go on to say that the less of imposing preferences by force on others, the better. So how about we, e.g., build that social safety net in some way other than passing laws and getting the state involved, shall we? (As for Republicans imposing their preferences on Democrats via force of law - making the Orange Man president for example - the Democrats' complaint would in effect have to reduce to: the wrong sets of preferences are being forcibly imposed and on the less deserving targets of forcible-preference-imposition. Which is to say, Democrats have cultivated lousy habits of thinking about politics so as to rationalize their ethically unidimensional fairness/equality ethos (and to ignore or strawman or weak-man the libertarian your-life-belongs-to-you-not-the-demos refutation of statism). In sum: politics is the art of the majority forcibly imposing its preferences on the minority. If people were more consistent in their revulsion at the element of force involved, and do their homework thoroughly, they'd be libertarians. (Much as Republicans have their weak spots - like, how did they nominate the Orange Man when Carly Fiorina's debate performance was more impressive? - they're closer to the libertarian mindset than are the socialism-lite Democrats.)
The element in common to both religion and politics is how the process of independent reasoned judgment is bypassed by authoritarianism in its epistemic and social manifestations.
Now that this simple explanation is out of the way, how about we try reason and freedom consistently?
