How do you make what you've liked private on this site?

People can see the tits I've liked... how embarrassing...

Settings > advanced > "Private favorites and votes"

You actually need to be Gold+ to be able to make your favourites and votes private. Unfortunately, Gold upgrades are currently unavailable, so you're out of luck.

Consider making a favgroup. You will still need a Gold level account or higher to private the group but it adds a bit more friction to see what you've actually favourited. Realistically few to no people are checking the profiles of Member level accounts directly (except in the case of promotion candidates or feedbacks for poor site use) and your own name will be lost in a sea of other names in the list of accounts that liked some posts if they have a high upvote count and you're early to upvote.

In other words, the golden rule being, don't call attention to yourself, whether it's on what you've liked or anything else. Add some friction to seeing your own favourites and no one really cares about what you've liked if it matters to you that much.