People are logically afraid that the way information is filtered by Yandex, their view of the world may become distorted and infected with Russian narrative. Let's say, try looking for anything about LGBT or the Orthodox church with Yandex, you will see stuff that looks coherent and is solely designed to bend public opinion onto the Kremlin side.
Yandex is Russia - OWNED, not just hosted there. That is, at least after the recent takeover and emigration of original founders, it is directly a state-sponsored propaganda tool fully in the hands on Kremlin, existing for the political purpose, not to make money.
It is same as using VK.com for social network for the reason that it has loads of pirated software, movies and porn (which is by the way true). You will slowly become just a walking product, and later a tool of Russian propaganda.
For this reason, i completely quit any sources of information in the Russian language, try to not use services with probable Russian association, and cut off all Russian contacts except those i have chances to pull out of there (and already succeeded with a few) - however toxic the model of thinking of these people is, i feel it's worth the risk because i am doing my part of weakening Russia by doing it.