I work in a public library. The one I used to had a DQST.
I think it's fair to say that there is a ton of tokenism, of all kinds, in libraries now.
Public libraries are of course meant to be accessible to all people and to support their interests and needs in terms of information access. They also have a strong mandate to be politically neutral and to maintain balance in their collections as far as reflecting all public views.
But a combination of political pressure and the fact that the majority of people working in libraries see themselves as politically progressive means that being inclusive has largely been interpreted as being a venue to push id pol, in much the same way schools have been.
It's a fine line, but behind the scenes I think it's pretty clear that this goes beyond just trying to respond to the community. Just as an example, the library I used to work at was very strongly taking that approach. When directed at the political level to concentrate programming on diversity, they came out with a list of 10 children's authors for branches to invite. All ticked some diversity box - not including being a woman in that - none were white. This is a region which is over 90% white.
As you might imagine, collection diversity was also poor - there was certainly a concentration on what were seen as marginalized voices, a full third of the YA books were queer oriented. But if you wanted to have political diversity in the collection you would not find it. (They were terrified about the possibility of having certain books on the shelves that people might be upset about.)
There are groups that don't feel all that included in the library any more because it is so clearly oriented to a particular progressive political view. When it comes down to it, you can't have an institution that is really inclusive - in the sense of being politically neutral - and also so committed to being a vehicle for social change, even what it sees as positive social change.