The phrase 'mostly believed that' is correct and can be used in written English.
You can use it when you are talking about a prevailing opinion or thought. For example: It is mostly believed that the sun rises in the East.
Barring a brief interlude in the ninth and tenth centuries, and a few modern liberals, Muslims have mostly believed that the Koran is distinct from every other communication.
Until about 30 years ago scientists mostly believed that their task was to find as many examples as they could to confirm their theories.
I mostly believed that Alex and I were just two people who happened to meet over some lukewarm Natural Lights and found each other attractive enough to be worth the effort to make more of it.
These patients mostly believed that participation in CTs was the best treatment choice and involved state-of-the-art treatments (46%).
Even where services were believed to be failing in their duty, however, young adults mostly believed that these services were not culpable for these failings.
Indian parents, he says, mostly believe that their children should become civil servants, doctors or engineers.
The airlines mostly believe that they will operate normally on Friday, although none are certain.
"European countries mostly believe that you just need to carry on the fiscal consolidation and economies will adjust," he said.
Skeptics mostly believe that prostitutes sell sex voluntarily, while anti-trafficking advocates sometimes suggest that they are almost all forced into the trade.
There is a gulf between present American policy toward North Korea (to the extent we have one) and the policy favored by most people who know something about the Koreas, who mostly believe that we should try harder to woo it out of its isolation.
