The phrase "to hold that belief" means to have a particular idea, opinion, or view about something in one's mind and to think that it is true or valid. Full definition
The results are generally consistent with widely held beliefs about supply - constraints. (nreionline.com)
And, while there's no hard science to back up this assertion, it's a commonly held belief in the veterinary community. (wagbrag.com)
But claiming these exceptions usually required a showing of evidence of deeply held beliefs; one couldn't legally avoid military service just by saying they didn't want to go. (law.stackexchange.com)