What is the duty of YouTube channel owners regarding comments that are offensive to religion or good, are they sinful because of them, and what is the ruling on leaving offensive comments due to their abundance?

You must alert your channel's visitors to avoid offensive comments and delete any that you come across, as this falls under the category of enjoining good and forbidding evil. There is no sin upon you for the existence of religiously impermissible comments that you are unaware of. If offensive comments become numerous, the safest course of action is to disable the comments feature.