All U.S. registered airlines have to operate Part 121 of CFR 14. 121.306 governs the use of portable electronic devices (PED). See below
121.306 Portable electronic devices.
(a) Except as provided in paragraph ( of this section, no person may operate, nor may any operator or pilot in command of an aircraft allow the operation of, any portable electronic device on any U.S.-registered civil aircraft operating under this part.
( Paragraph (a) of this section does not apply to—
(1) Portable voice recorders;
(2) Hearing aids;
(3) Heart pacemakers;
(4) Electric shavers; or
(5) Any other portable electronic device that the part 119 certificate holder has determined will not cause interference with the navigation or communication system of the aircraft on which it is to be used.
© The determination required by paragraph ((5) of this section shall be made by that part 119 certificate holder operating the particular device to be used.
The 119 certificate holder is the airline. So it is on the airline to determine which PED can be used. The airline has to prove to their local FAA principle airworthiness inspector (PAI) that the PED meets 121.306. That is where the problem lies as to why some airlines allow the uses of your GPSR and some don't. A new PAI shows up and they question the whole PED program and you get to start over.