The phrase 'many believe that' is correct and usable in written English. You can use it when expressing a general opinion or introducing a statement based on opinion. For example: "Many believe that people should have a better work-life balance."
How many believe that is another matter.
Many believe that Trump is basically bluffing.
Many believe that Roma are only a social group.
Many believe that sleep deprivation among women has worsened.
Many believe that Carlsberg just needs to tweak its terms.
Many believe that preservation of the native ECM structure during decellularization is highly desirable.
These examples may seem fanciful in a world where many believe that might makes right.
MOST governments try to keep prices down and many believe that competition helps.
Many believe that Snider is the most powerful figure in hockey.
Many believe that relativity prohibits superluminal signaling of information.
Many believe that Android is an open platform.
When I feel like I can't trust my brain 100%, Ludwig really comes in handy. It makes me translate and proofread faster and my output more reliable.
Claudia Letizia
Head Translator and Proofreader @ organictranslations.eu