Um.....my DS's Kindy has a doll corner. A typical setup of kitchen set, doll crib, possibly table and chairs, high chair....it's a house/doll corner with baby dolls.
They also have a dollhouse, but it's a doll family not Barbie.
their other "free choice playtime" choices (that I have seen when I am there) seem to be all games, puzzles, and some building toys. (my son loves these big things called "Wedgits" he picks them whenever they are a choice. There are cards and you can try to build their ideas or do your own. He likes to try to do theirs.)
I also have seen a sand/water table but they don't use it the afternoon I am there.
They seem to rotate their "free choice" days, a couple different options but not ALL of it ALL the time. (my personal thought on this is that it's to help the kids try out different things--if the dolls are *always* an option, some kids would *always* play that. We did something similar when I worked in a preschool classroom with the computer--it was only available ONE day because we had kids who would choose to do little else. We wanted them pretending and interacting with *humans* more than screens.

We also had a specific time after 'circle' where the children could choose to write at the whiteboard, use the writing center--coloring sheets, paper and pencils, stencils, tracing sheets etc. or "read" books on their own or be read to--because the kids didn't typically choose these things at 'free play' and we wanted to encourage them to try them out. They still had choices, but limited.)
DS's preschool had a lot more toys because they had about an hour a day dedicated to free choice play...but still not much if anything in the way of "licensed characters". They might have had a cowboy hat and boots in the dress up corner for example, but not a "woody" or "Jessie" costume specifically. They did have all sorts of vehicles including matchbox type cars. I don't recall ever seeing Barbie, but definently dollhouses and family dolls. And of course all kinds of art supplies. And some sets that rotated--stuff like a doctor kit, different dress up clothes etc. And of course your typical 'kitchen corner.' Blocks.
But....*I* played with my Heart Family barbies like lots of kids play with the family dolls.....I wouldn't object to them until I saw exactly what was available to them.