Interesting. So I've now bothered to look and indeed, Reddit offers the following controls. This reminds me that they're also giving a government-connected Chinese company (as part owner) this stuff:

[ ] make my votes public

[ ] allow my data to be used for research purposes

[x] don't allow search engines to index my user profile

[ ] allow reddit to log my outbound clicks for personalization

[ ] let others see my online status

This is one reason I did not renew my premium account years ago, as there reports that the special service also tracked all of my browing history