ZAB Controller reported the complexity and workload levels at sectors were unsafe due to scheduled GPS jamming causing navigational errors and frequency congestion.

Narrative

We had weather today with a high volume workload due to additional weather in the Houston metro. This caused more aircraft to be routed into the area and cause our numbers to be near or above most of the morning and early afternoon. Starting at XA30; GPS jamming from White Sands started and immediately aircraft started to take over the frequencies and talk about losing their ADSB and transponders. Multiple controllers on sectors quickly asked the supervisor to 'stop buzzer' because the complexity and workload was increased to unsafe levels. The supervisor talked to the Operational Manager about stop buzzer and it didn't take affect until at least 30 minutes to an hour. I'm not sure how long it took; but I called the OMIC (Operations Manager in Charge) line directly to talk to the Operational Manager; but it was forwarded to TMU (Traffic Management Unit); which was both frustrating and surprising. I had an aircraft almost deviate into the range because they were having navigational issues and I had thought that jamming had stopped. We were also told before the shift when our supervisor went to standup briefing that there would be no jamming. When multiple controllers ask for stop buzzer and there is no response it shows how both unprofessional and how disrespected the controllers feel. If they don't trust us with stop buzzer; then why have the ability make the request? Also; why is the OMIC line forwarded to TMU? We can't even have a direct line to the Operational Manager and have to go through a third party just to get ahold of them.If a request is made by controllers; why is it questioned so much? They don't trust us to make a decision and would rather us work in unsafe situations with complex and high volume traffic.