Is the Bluebird Cafe ok for kids ages 6 and 4?

There were no kids when we were there, so unless they can remain quiet for an hour during the performance I would say no

I would agree it depends on how quiet your kids are. There weren’t any kids at the show we went to and our kids would have been too loud.

If they can be quiet during an hour performance then yes. There is a "Shhhhh" request while performers are playing.

As mentioned the focus is on the music so the preference is for quiet. Took my 9 year old and he was barely able to make it through an hour of music so plan accordingly.