Reddit is not a US government entity, so the US constitutional right to free speech is generally not applicable to discussions of Reddit.
The exception is the case where a US government entity controls an account that is a mod of a subreddit, in which case they would be subject to the First Amendment when performing mod duties such as deleting user comments or banning users. This specific case would burden only that user and would not place any additional burden upon the non-government mods or upon Reddit itself or its admins.