People may use critical thinking while doing politically related things. It may be harder than using critical thinking in science because we have to consider human relationships which may be harder to define. But there is also a particularity of politics related to polarization and choosing sides.
Consider Democratic and Republican parties of US, if you stick to one of them and if you support some of their principles, you are expected to support the rest of them. So if you prefer progressive taxation and liberal principles, you can be considered a democrat. Then other people may expect you to support gay marriages and universal healthcare. If you criticize some ideas from a Democratic agenda you may fall into a political limbo and become an independent person.
The same could happen if you stick to some of Republican ideas, but not for all of them. And in case you support some ideas from one side and some from another side, both sides may consider you an apostate. As a result, you may find only a little support because you don’t have a distinct political label.
I imagine that not every member of the Democratic party support every one of their principles. Even if they stick to a major party group like New Democrats they still may like only some of shared ideas. But at the same time people tend to avoid thinking when they can do that, so intellectual laziness leads to sticking to the same political agenda even if a person doesn’t really like some of separate topics.
As a result political parties support intellectual laziness because laziness makes them more stable. If people think more and start question a set of their values, these values may need to be changed thus creating more groups inside a party or even splitting it. Acquired intellectual laziness can even spread to other areas making people more conservative and prone to keep their beliefs.