You definitely can.

You just need to login to reddit in a browser quickly and make a private subreddit.

Third party app and NSFW access restored: they seem to have excepted mods from the changes

If you’re self hosting (i.e. running it for yourself, your family members and maybe some friends), your use would fall under GDPR’s household exemption

does not apply to … the processing of personal data by an individual in the course of a purely personal or household activity

Thats Article (2)(2)a.

Of course, if you’re taking money or making it available to the general public it’s a different matter.