RBMK reactors are terribly unstable at low power levels. The other three units (obviously) still had fresh fuel in their reactors. Trying to SCRAM the units and keep the fuel in the reactors at low power levels for extended periods of time could have been more dangerous than keeping them running. Not to mention the fact that Unit 4's problems were (partly) a result of trying to keep the unit running at low power levels. Why then would one put the other three units into a potentially similar situation? You wouldn't. With RBMKs, the best option is to keep them running 100%.

Once Unit 4 was cleaned up/stabilized enough, there was really no reason to shut the other units down. Refuelling would then proceed as normal (or normal enough, all things considered).

I believe Russia still has 11 RBMKs in operation, plus a few more in other countries. There was plenty of public outcry to shut down all RBMK reactors, which I personally agree with. Some were decommissioned, eventually. The RBMK is a very unstable design and easily enters unsafe conditions, however afaik, upgrades and changes have been made to the units themselves, and to operational procedures to attempt to prevent the same situation that destroyed Unit 4 at Chernobyl. I don't know enough about said upgrades to say how much safer the remaining RBMKs are now.

I do know that RBMKs are inherently dangerous (though simple). Although you can do things to upgrade them to make them safer, you can't change the principals of how they work, and I don't think they're as safe as the PWRs and CANDUs used around the rest of the world.

That last bit is just personal opinion based on experience. I work at Palo Verde Nuclear Generation Station, so it's not like I'm just blowing smoke out of my ass or anything, for whatever that's worth.