It's a strange limitation to place on the utility of reason to say that it should be relegated to domains which have less immediate affect on human life. Poltiics are immensely important.

One of the points of Eliezer's article, IIRC, is that politics when discussed by ordinary people indeed tends not to affect anything except the discussion itself. Political instincts evolved from small communities where publicly siding with one contending leader, or with one policy option, and then going and telling the whole 100-strong tribe about it really made a difference. But today's rulers of nations of hundreds of millions of people can't be influenced by what any one ordinary individual says or does. So our political instinct devolves into empty posturing and us-vs-them mentality.

Politics are important, sure, but only in the sense that what our rulers do is important to us. The relationship is one-way most of the time. If you're arguing about things that depend on what ordinary people do - such as "shall we respect women equally in our daily lives?" - then it's not politics. But if you're arguing about "should women have legal suffrage?" - and you're not actually discussing a useful means of bringing that about, like a political party (of men) - then the discussion will tend to engage political instincts and get out of hand.

If rational discussion only works effectively in certain domains, perhaps it is not well developed enough to succeed in ideologically charged domains where it is badly needed. Is there definitely nothing to be gained from attempting to reason objectively through a subject where your own biases are most intense?

There's a lot to be gained from rationally working out your own thoughts and feelings on the issue. But if you're arguing with other people, and they aren't being rational, then it won't help you to have a so-called rational debate with them. If you're looking for rationality to help you in such arguments - the help would probably take the form of rationally understanding your opponents' thinking, and then constructing a convincing argument which is totally "irrational", like publicly shaming them, or blackmailing, or anything else that works.

Remember - rationality means Winning. It's not the same as having "rational arguments" - you can only have those with other rationalists.