But us westerners usually don't care much about that kind of censorship because it doesn't affect the searches we normally do. ("normally" as in "we usually don't search stuff about russian politics")

How about if you do searches about history? In Russia, it is explicitly a crime to portray the "Great patriotic War" as anything but noble, wonderful, and a huge russian success story. Multiple game developers have active warrants for arrest in russia because they put a russian tank in their game that isn't OP, or have a campaign that accurately demonstrates an unsavory thing the soviets did in the 40s.

While I was still living in Russia, llvm.org was blocked for several years because fuck you we balling.

It looks like the best solution is for “westerners” to use Yandex and everyone else to use Google or Bing and this way they can search with less targeted censoring on their terms.

Are people in Russia allowed to use Google? I thought Russia has been locking down their Internet for a while. Not as bad as China, but still missing anything unflattering to Putie.

Google properties are still unblocked, for now. But, yes, Internet censorship in Russia went into overdrive with the invasion.