I, uh, just bought it on Switch, problem is it won't let me play without a Battle.Net account. I don't want a Battle.Net account!

This comment bothers me enough that I had to reply. Diablo 2 requires a battlenet account. Ever since the original Diablo 2 launched 20 years ago, it required a battlenet account. The two are intrinsically tied together, designed together. There would not be any other way to play D2 multiplayer without it. If there's information you don't feel comfortable uploading for your battlenet account, then create a gmail account or something and give them fake information so you can still log in.