You should be able to paste instances into the explorer even with a script open. (This functionality existed prior, guessing this is a new issue due to the new explorer Beta)
This was a bug with the new exploror, but I guess its also on the old one (the bug has been reported many times, and the devs are finding a solution I think)
Easy fix thats works for me: Try copying something random with Ctrl + V / Ctrl + Shift + V and see if it copied. If yes, it should work. Otherwise, you should check the settings of Roblox Studio or your PC.