I had the same concern for using zerotier, and not wanting to use a vpn with holes through my router. I had a bunch of errands around my local town (small mountain town in Colorado), so i decided to test on my iphone (verizon) that has zerotier installed …
totally open public wifi: public government building. Library, grocery store, city park - no issues
Open with portal acceptance: sandwich shop, police station (in parking lot), coffee house - no issues
public wifi with password: another sandwich shop, anytime fitness gym, true value hardware store, another small grocery store - no issues (although true value took three tries to connect on zerotier. Once connected
blue iris app worked as normal)
I had also used zerotier previously using a a captive portal at an RV campground. No issues and blue iris app worked normally. (Captive meaning portal login page comes up, you agree to their service and can purchase extra speed ($5.00) for your one device for 24 hours).
Zerotier also has worked fine using the blue iris app on verizon throughout a few surrounding states.