You make a deal - they stop it so that they may be granted a Firefox monopoly on advertising. Then, site operators are left with a choice:
1) abandon tracking, earn ad revenue from Firefox and Chrome
2) keep tracking, earn no ad revenue from Firefox
Yandex ads will be more pleasant due to not having the large amounts of tracking, meaning they'll reduce page views less. As a result of blocking ads, Firefox will become much more pleasant to use. As a result, the first option will be more profitable.
Yandex' "other concerns" is the whole point - they are the only serious competitor to Google. The enemy of my enemy is my friend. If you were to enter into such a deal with another American/European company, the regulator would crush them over antitrust concerns. This leaves Yandex (or the Chinese) as your only options.
"In fine, let us recognize that the adoption of my advice will leave us each citizens of a free state, and as such arbiters of our own destiny, able to return good or bad offices with equal effect; while its rejection will make us dependent on others, and thus not only impotent to repel an insult, but on the most favourable supposition, friends to our direst enemies, and at feud with our natural friends." –Hermocrates