"There was new activity in [studio]" notifications aren't invites, and aren't sent by your followers. They're sent to you automatically if there was activity in the studios that you are already in. (Any new/removed projects, comments, edits to title/description, or additions, promotions, and removals of studio members). Invites are when somebody wants you to join a studio you are not already in, and they can only invite you once, so you shouldn't be getting multiple over and over again. Dear ST,
I really love Scratch, But there is 1 problem. My followers keep on sending me studio invitations and i keep getting useless notifications! Here's what it says: There was new activity in (studio) today! So ban a user and all their studios if they keep on sending you invitations when you didn't ask to join the studio!
Still, I agree that for actual invites, something should be done about somebody inviting you to so many studios even after you don't join any of them. They shouldn't be banned, but maybe they get an alert telling them to stop, or they are temporarily unable to invite people.
They usually invite you when inviting their followers, so if there's one person who keeps inviting you, then you can consider if it's worth unfollowing them.
Here's a suggestion for being able to disable getting invites: https://scratch.mit.edu/discuss/topic/71242/
For a more universal solution to all of this, there's a topic about filtering messages in general (so you can filter out the ones you don't want) https://scratch.mit.edu/discuss/topic/56422/