Ok here is how it works.
US CDMA Carries (VZW, Sprint, etc): Use SIM cards on LTE enabled phones. The SIM Card uses LTE for data, voice and text on older CDMA networks. Instead of having to manually register the phone on the CDMA network, the LTE SIM card takes care of that in the background. Verizon's network would never allow it, but it's conceivable that you could find a GSM phone that is compatible with VZW's LTE bands and the data would work (again, they don't allow this).
US GSM Carriers (T-Mobile, AT&T, etc): Use SIM cards to register on the network (GSM, HSPA, LTE, etc). If the frequencies are compatible, the phones are compatible.
Now with the advanced cellular chips, its likely that one chip can handle GSM/LTE and CDMA, however they are not licensed by QUALCOMM to do so, so the abilities are disabled in the firmware.
Until everything runs off of LTE (VOLTE and messaging on LTE), you will not be able to use a purely GSM phone on US CDMA carriers.