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There's only 11 official trappist breweries so assuming it had those the following produce vegan-friendly beer:
Brasserie de Rochefort
Brouwerij der Trappisten van Westmalle
Brasserie d'Orval
Bières de Chimay
Brouwerij de Koningshoeven (La Trappe)I think Achel is also vegan but can't find confirmation at the moment. The other 5 aren't Belgian so I'm not sure what the deal is there and I don't think I've come across their beers to bother checking.
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The monks might be vegetarian, but is the beer vegan?
The vast majority of Belgian beer should be vegan. If it's not, that should usually be down to ingredients like honey, which should be easy to infer from the beer's publicity or name, I think. There is very little tradition on the Continent of putting animal ingredients in beer (unlike wine).
The monks might be vegetarian, but is the beer vegan?