To expand, on Lawrence's answer, I think it requires some flexibility. How much depends on you and the others organizing the particular book fair in question. I don't think it always works to draw hard and fast lines (though I agree with Lawrence about explicitly statis communist or socialist groups - they can have their own book fairs).
At the book fair I have helped with we chose (at different times) to exclude groups that were not anarchist (Marxist groups, activist groups, etc) or to include other non-anarchist groups (anti-state communists or activist groups who anarchists in the area have developed deeper understanding or affinity with). We've also excluded "anarchist" projects based on history of being asshats, acting in a similar way to front groups, have refused to address concerns about past behavior, or who are just sketch-as-fuck.
As far as Haymarket Books, I suspect we would've said no, since they are pretty explicitly a Marxist-Leninist publisher, but I am one person, and would've wanted to hear input from others involved in organizing it.