In order to help you answer this question, let me first of all address what is meant by the term hegemonic masculinity. In a nutshell, hegemonic masculinity "explains how some men make it appear normal and necessary that they dominate most women and other men" (source listed below). In other words, it describes a situation where men do not only feel superior to women, thus justifying being the dominant gender, but also feel superior to other men: men whom the leading men consider as weak and almost feminine—for example, homosexuals.
With regard to how this can be observed in religious institutions, you could use the Roman Catholic Church as an example. Here, even today, women are not allowed to become fully accepted priests. Women have been fighting for decades trying to be able to play similar roles to men in the Catholic Church. There have been some advances in recent years: for example, girls are now allowed to help as altar servers, which was a role solely reserved to boys in the past. However, overall, women are still definitely having to negotiate hegemonic masculinity.
With regard to nonheteronormative people, you could also use the Catholic Church as an example of how this group of people has got to fight against hegemonic masculinity. For example, homosexuality is still not accepted in the Catholic Church. This means that homosexuals are not allowed to work for the Catholic Church.