There’s a long history to this, going back to Eastern Europe and the historical role of Jews in European society.
Keep in mind that in Europe, because of the endemic anti-semitism as far back as the 1800s and before, there were many jobs that Jews were simply prohibited from taking. So Jews, in general, had to find jobs in industries and shops that were legally permitted to them. One of those job areas was (broadly defined) drama and theater.
Yiddish theater was thriving all over Eastern Europe – Poland and Lithuania, and to a lesser degree Germany, had strong Yiddish cultural institutions, including drama, theater, comedians, books, and so on. And, of course, there evolved famous Yiddish/Jewish actors and directors and so on.
Two major political things happened: Jews got thrown out of Russia in the 1890s-1920s, which was all part of one of the major immigration waves. (Irish, Jews, lots of ethnic groups left Europe at that point. And of course in the 1939–1945 time frame World War II and the Holocaust created a second wave of Jewish immigration.
Many people emigrated with nothing but the clothes on their back – they didn’t have riches or factories. But they did have their Yiddish / Jewish culture, which they rapidly reinstated in the Lower East Side of NYC and eventually Hollywood. That, in, turn gave rise to movie studios owned and run by Jews, and other entertainment venues and opportunities.
So in a weird and twisted sort of way, the east-european antisemitism of the 1800s is largely responsible for the role of Jews in TV and Movies today.