It's also worth noting that unlike college fraternities in the US, which seem to be pretty ubiquituous, Burschenschaften in Germany are fairly niche and all vee

It's also worth noting that unlike college fraternities in the US, which seem to be pretty ubiquituous, Burschenschaften in Germany are fairly niche and all veer to the right wing of the political spectrum: mostly Christian conservatism although there are widespread völkisch nationalist undertones. I'm not saying these are "nazi" groups but I've yet to encounter a Burschi who isn't at least to the right of the general public. As the StackExchange answer suggests, membership is also often tied to military service (which also is much less common than in the US) and the culture is strongly tied to aristocratic (or at least "old money") lineages and "mentorship" (some would say nepotism). Basically the correct mental image is probably private societies in expensive English "public schools" (i.e. what most of the rest of the world would consider private schools: the kind you have to pay for), not US style "Greek houses". It's worth noting that despite the similarities between völkisch nationalism and ethnonationalism, most Burschenschaften are explicitly opposed to the far right, at least in public statements. If you want to tie them to an anti-democratic movement it's probably more likely to be neo-feudalism (e.g. the Reichsbürger monarchists) than actual neo-nazis. There have been some instances of nazi chat groups within Burschenschaften being found out and members have been running for the far-right nationalist Alternative für Deutschland party however. EDIT: Also, worth noting, schlagende Verbindungen, i.e. the ones engaging in ritualistic duels with sharp blades, are on the fringe of these groups and also veer to the right of those (I think most "moderate" Christian conservative ones are strongly opposed to the practice). So the entire dueling thing nowadays is a fringe of a fringe of a fringe and most Germans would feel very concerned if you tell them you engage in it.