I use an iPhone (and iPad) with Safari, plus a few other 3rd party browsers for them. I haven't seen that message on them.
Remember, we're now an SSLencrypted web site... more here:
Security Improvements - January 2017 Update
So, your phone's Internet browser needs to support several security protocols and their associated certificates to handle that capability.
Also, in some cases, people use 3rd party app browsers on their phones and tablets that aren't supplied by the original phone manufacturer.
I don't know what your circumstances are, but regardless, I would suggest your safe bypassing the message.
For privacy, if you want to PM me more details I'll look into the specifics for you.
Regards,
Doug