They may use whatever time they want. But very few people know that GMT is in danger because International Communications Union wants to abolish leap seconds. Leap seconds are meant to keep atomic time with astronomical mean time which is sometimes irregular due to small variations in Earth rotation. A leap secomd is added or substracted from UTC measured by atomic clocks when the difference comes close to one second. The adjustement is generally done on June 30th or December 31st. If this is abolished, mean meridian will shift gradually and civil time will no longer be tied to astronomy.
We must defend GMT for practical reasons. Atomic time without correction poses a problem for amateur astronomers.
Now, when did the Chason Ish live, and what is his argument to use "Jerusalem Mean time"? In fact, mean time is a scientifical invention to keep time by clocks of uniform speed because real sundial time fluctuate throgh the year. And the use of " x city mean time" instead of local mean time is an even newer scientifical invention to keep a reference and have the same time in a given territory. I doubt Jerusalem Mean Time would have any relevance in Hallacha.
In fact, shortly after establishing the rule of each country having the mean time of its capital, it was decided to use a world reference and countries would have either that world reference meridian time or a difference of entire hours. Three spots were proposed to be Merdian 0: Jersusalem, Paris and Greenwich. Greenwich was approved out of the three in 1885. It was the most practical because the date change line would pass through relatively unpopulated regions of the Pacific Ocean , thus allowing America, Europe, Africa and Asia and Oceania to have the same date.