There is no open door policy with NATO. Russia and the Soviet union have tried to join NATO at least a few times publicly and were rejected every time.
What's the point of NATO again?
The point of NATO is exactly why Russia fears it - consolidated strength that makes it impossible to pick off member states one by one by a stronger power (namely Russia). Russia and the USSR weren’t invited because they explicitly were the threat.
Wouldn't that explicitly prevent them from doing just that? Also, so far NATO has been used to bomb Yugoslavia and Libya. It appears it's NATO doing the picking off, doesn't it?
In order to join NATO, one of the current requirements is having a liberal democratic government with civilian control over the military. Russia (and the old Soviet Union) didn't meet that requirement.
Perhaps Russia should try transitioning to becoming a liberal democracy first?