I've stayed in a bunch of hostels in Mexico, some really nice ones, but again with covid I'm sure all will change until it's sorted.
I don't think there are any
Hosteling International hostels in Mexico. Guidebooks like
Lonely Planet as well as many individuals often refer to places which offer inexpensive shared accommodations and cooking facilities as "hostels", but most of them aren't part of the
Hosteling International network.
World map of
Hosteling International locations:
https://www.hihostels.com/explore
Years ago, I stayed at an "official" hostel in the Loire valley in France, with a couple of friends while we were touring. There were 3 notable things about that hostel, which were indicative of the contrast between official hostels in the USA and France: This particular French hostel had outhouses, rather than indoor toilets. It had a fantastic restaurant-quality kitchen. And they sold local wine out of a cask for a very cheap price per pitcher. Alcohol was completely banned in American hostels, at least at that time.