If you are a Russian citizen and acquire U.S. citizenship, it does not mean that you automatically lose your Russian citizenship, because according to the law, no one can be deprived of his or her citizenship, except on his/her application (officially restored). Russian law does not prohibit you from having more than one citizenship, but only considers you to be a Russian citizen and therefore requires you to enter and leave Russia with Russian passports.
As a state institution, the Consulate General ensures compliance with state law, so each person whose foreign passports or travel documents indicate his/her place of birth as "Russia" or "USSR", or one of the states that made up the former USSR, will need to provide evidence of the absence of Russian citizenship.