Yes, it turns out it wasn’t a MixPanel issue at all. One of us was running the DuckDuckGo chrome extension, which blocked the sending of Users and Events to MixPanel. The fix is to disable the DuckDuckGo extension when testing our app.
Yes it seems that more and more browsers are blocking client side tracking like Mixpanel. For example, by default Google Chrome has a Do Not Track feature that will block Mixpanel.
I think the solution is to use server-side tracking like Segment, which can then be sent into Mixpanel.