You are a business.
You forgot one word. Jewish. This is a Jewish business which by extension falls under the strictures of Jewish business practices. To be more specific, this is a Jewish business that caters to the Yeshivish community in particular. That means it is incumbent upon the administrator(s) of the site to monitor and yes, moderate their site according to the customs and taste of the community that they serve.
You may or may not have noticed, but the name of the site is The Yeshiva World, not The Jewish World. This is not by accident.