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can't go wrong with anything German because purity laws...
I think that applies to 99% of German beer, but it is possible to get special permission to add other things. I can't remember where I read it, but I think there are a (very) few German beers that are not vegan. That shouldn't be an issue, just a reminder that (as with everything in life) it's not 100% sure.
Having just re-read the German Wikipedia article, I also think the 'purity laws' (see below) were not hugely relevant for veganism; the issue only arose in this country because of the various conventions for clearing beer. That never seems to have been done in most of Germany, and certainly not in Bavaria, although the issue seems very different with wine. I've long thought that isinglass only became so prominent in Britain because of the large amount of waste from the fish corpse industry, and the consequent availability of cheap fish gelatine. I suppose in Germany they could have used other kinds of gelatine, but I don't know how well they would have worked. It seems that now a substance called PVPP, a kind of plastic (Wikipedia doesn't say what it's derived from) is permitted for 'beautifying' beer.
The 'purity laws' were originally all passed for other reasons--to give Bavarian brewers a competitive advantage (for instance, against "Grut" beer, that is, beer brewed with various herbs, which was widespread especially in Northern Germany and the Netherlands; I'm afraid I don't know the English word for "Grut"--the Dutch term "Gruit" seems to be being used internationally, and there is a Scottish beer called Grozet Gooseberry, so perhaps 'grozet' is an English or Scottish word for it), to guard against certain intoxicating/hallucinatory effects caused by certain ingredients used in the Middle Ages, to keep "Süßbier" ('sweet beer') made with added sugar out of Bavaria, and to prevent grains like wheat, which were seen as more valuable than barley and needed for bread, from being used for beer. Interestingly, apparently in the Middle Ages the most widespread grain used for beer was oats.
On a side note, the term "Reinheitsgebot" appears to be a 20th-century coinage (many people think it dates back to 1516, but it's first attested 400 years later), and a "Gebot" is not a law, but an order or a standard, albeit contained in various laws (that typically regulated much more about beer than just the ingredients).
Of course, it is good that most German breweries still adhere to certain "Reinheitsgebote" (plural as there are so many versions of them) voluntarily, although there was also an article in the 'London Drinker' a while back, by someone not concerned about veganism, who argued that "Reinheitsgebote" had stifled innovation in brewing and reduced diversity in German beer by mandating against quirky local beers, some of which are apparently being rediscovered and brewed again in small batches, undoubtedly using the above-mentioned possibility of obtaining special permission. As far as I recall, non-vegan ingredients were mentioned there, although all ingredients mentioned in the Wikipedia article that were variously prohibited in the Middle Ages were vegan (mostly herbs).
I approve of any breweries that actually do vegan beer these days... can't go wrong with anything German because purity laws... plus it's Oktoberfest soon so all the good fest beers are out. In this country, Verdant are held very highly as it always says if the beer is vegan or not on the can... I've not seen one that isn't vegan yet actually... they love brewing very dank, heavily hopped beer... if you can find any online, Leigh on Sea Brewery only brew one non-vegan beer, I love everything they do and they're local to me which is even better.