Indeed your Republic number is not “wireless”. It would best be described as mobile VoIP. Context follows:
Republic numbers are classified as Voice over Internet Protocol (VoIP). Republic’s use of VoIP is part of the nature of its’ blended WiFi/cell service. According to the FCC, VoIP numbers are landlines (wireline is the more correct industry term). There is nothing Republic can do to change this regulatory classification.
Your Republic number is fully capable of receiving both calls and text messages. Regrettably, some service providers refuse to recognize this. Republic cannot control the policy decisions of others.
Sadly, it would seem your ISP has yet to join the rest of us in the 21st century. You might try contacting their support and ask that they whitelist your Republic number.