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Seems like a common occurrence lately with a new update? Maybe @Mobility_Princess knows something.
Ever since a recent update pushed out I am having the exact same issue when I am using VPN.
So to test if it was the VPN service or the phone I used 3 different VPN apps, they all caused the same issue. So I Factory reset my phone and set it up as a new phone, I made sure to only install the VPN app and tried again and I am having the exact same issue still.
I should note that before this recent S6 Update I could send and receive MMS while on VPN.