I am a great fan of Haydn’s music, especially since I find his piano sonatas very playable!, but I didn’t know that Haydn was accepted into the Freemasons. I have tried searching for a list of banned authors, and his name does appear on a few, but I don’t know how reliable these lists are (since they’re not ‘official’).
It is not inconceiveable that his works may have been banned from performance in the liturgy since there was a major crack-down on freemasonry by the Church in Haydn’s time. However, the works themselves were not heretical - it’s not as if he changed the words of the Mass or something, and indeed he wrote some of the greatest Mass settings the world has ever seen.
Is it possible that the Dictionary means that the works can’t be performed in the liturgy for purely practical reasons? I know his ‘Missa Sancti Joannis de Deo’ is not too long, but some of his greater Masses simply would not fit in to the modern liturgy. Remember that when Mozart was Master of Music at Salzburg Cathedral, the archbishop ordered him to compose shorter Masses in order to keep Mass to 45 minutes… so it could very well be that in a liturgical context, performing a whole Haydn Mass wouldn’t go down too well with the congregation.
Whatever the reason (it certainly isn’t because the works themselves are liturgically incorrect), I doubt that any bishop would prohibit the performance of a Haydn Mass during Mass as long as it isn’t too long

Also, if you think about it, church music would be all the poorer if we were to cut out all the hymns, Masses and motets which were written by heretical (non-Catholic) composers, even though the most important part - the music itself- was top class, prayerful and liturgically sound…