Yeah this is straight up reactionary shit. They say it's not meant to persecute people with different sexual orientations, rather just target "the movement", but wtf does that even mean? How do they even legally define what "the LGBT movement" is? Do they think that people are card-carrying members of some official LGBT organization? This is so vague that it allows basically any interpretation that they decide is politically expedient at any given time.
Depending on public opinion this could range from being virtually a nothing burger that will only be used to go after western sponsored political opposition groups (which would be foreign interference anyway, Russia already has laws for that), all the way to making life a nightmare for queer people and trying to completely erase them from public visibility. Basically what will happen is up to what the mood in the general Russian public is at any given time and how much pushback there is when the government oversteps, but unfortunately at the moment a lot of Russians have very reactionary views on this subject.
The sad part is that i'm not sure that the outcome would be any different even if the ruling party was a communist one, at least if it chose to tail the masses on this issue. It's a difficult problem to solve because a vanguard party should not be tailing the masses but it also should not impose completely unpopular policies that the masses are not yet ready for. The correct thing to do is to prepare the people for more progressive policy with a thorough campaign of education and normalization.