ZAB Center Controller reported planned GPS jamming in their sectors near the TXO VOR caused an air carrier and other aircraft to experience navigation difficulties.

Narrative

There was GPS jamming going on near the TXO VOR. I took the position around XA30 and immediately started seeing target jumps that I initially considered a radar issue. I questioned the pilot; and he said he thought he was on course but was having issues with his GPS. After turning that into the Controller in Charge; I started having multiple pilots report issues with failing ADSB equipment and their GPS's not working. While taking these reports; an Aircraft X flight going to ZZZ reported that he would have to come off his RNAV routing if the GPS jamming did not stop. During and after this interaction with the Aircraft X flight; the Supervisor in the area was on the phone; working on coordination for another sector in the area. Feeling that safety was degrading; I called the Operation Manager on my VSCS (Voice Switching Control System) only to find that it was forwarded to TMU (Traffic Management Unit). I asked the TMU to have the Operations Manager call me; not understanding why the line was forwarded to TMU in the first place. After hanging up; multiple pilots said they had GPS and ADSB issues. I called the Operations Manager again; and the line was still forwarded to TMU. I asked to relay to the Operations Manager that the GPS jamming needed to stop and that aircraft were advising they would potentially have to come off their route.After hanging up; the Supervisor in the area finished his phone coordination and left the area to discuss the situation; only to return with the understanding that the Operations Manager had decided to continue the GPS jamming and not 'stop the buzzer' because the aircraft still had other ways to navigate. This decision is not the process that has been repeatedly briefed to the workforce. While not as severe as some prior GPS jamming events; tonight's events were unsafe and could hurt people in a more severe or complex situation. This issue has been going on for years at ZAB. There have been multiple briefings on the order; with several serious conversations with the military on the effects of GPS jamming. It has been repeatedly briefed to our facility that if jamming is affecting one aircraft; much less multiple; they are to stop the jamming operation and 'stop buzzer.' The Manager On Duty deciding that the effect on the plane wasn't severe enough to stop jamming is alarming. Someone not flying the plane nor working the positions taking the equipment failure reports should be deciding to continue jamming. Someone will get hurt ignoring the pilot reports or deciding for pilots how much equipment can fail or be unreliable before they 'agree' or decide to stop GPS jamming. Suggestion: Stop GPS jamming when aircraft equipment starts to fail or is unreliable. Retrain Operation Managers on how critical a situation is when equipment fails or is unreliable in an aircraft. Follow existing protocol for GPS jamming and 'stop buzzer' procedures. Brief the workforce on the process to stop GPS jamming.