I am the moderator in a game that has a category which requires a major glitch only possible with high clicks per second. Another runner wants to add a category in which autoclickers are allowed. My problem with this is that it removes any human input in the Run besides 3 clicks. This isn't allowed because of Speedrun.com's rules on modifying games using external programs, right?

The speedrun.com rules for that basically just mean that, if a game's rules don't specify otherwise, you are to assume that autoclickers are not allowed. However, games can make exceptions to these general rules as they see fit.