Would you say the same thing of Cultural and Religious Conservatives in the US?
Russia is very unlikely to use morality as a weapon of the state. It's not needed when you have the GRU.
Besides how do you make morality a weapon?
American conservative morality is allowing people freedom. Freedom of speech, freedom of worship, freedom to own a gun. If morality becomes you have to say what I tell you to say and you have to believe what I believe, it is now a totalitarian system.
A free nation will be moral as long as it is free without a need for a top down moral decree. For hundreds of years the US remained moral despite being a free nation. A totalitarian nation with a strictly enforced moral code will not only be not free, it will not be moral either. Look at Russia, massive alcoholism and drug abuse, rampant prostitution and one of the highest abortion rates on earth. No amount of moral decrees from the KGB spook in the Kremlin will change that.