I don't have any trouble receiving SMS messages from short code senders to either my Google Voice or my VoIP number. Is this problem specific to Twilio?
Sometimes sites want to know my mobile provider (why does it matter?), so I just choose Verizon or Other.
The only site that won't accept my GV number is att.com. Oh the irony...
I find sites that won't accept my Google Voice number on a semi-regular basis. I think the most recent was Uber, which I discovered when moving phones a few months back.
I wonder if I have more success because my GV number was originally a cellular number (many many years ago). I've used it with Uber and Lyft successfully.