Hey, @harmod Welcome to Spotify Community and thanks for reaching out here!
You can disable some options on your Spotify settings. On your phone app:
On your home screen, go to Settings
Scroll down and on the Social field, disable the options "Listening Activity" and "Recently played artists"
In addition, if your Spotify account is linked to your Facebook account, it's also recommended that you unlink them. Just follow it, on your desktop app:
Go to Settings
Scroll down and on the Social field, tap the "Disconnect from Facebook" button.
You can also do it on your desktop app settings:
Disable the option "Make my new playlists public", and then all your new playlists will be Secret by default.
Currently, there is no way to avoid that anyone follows your profile on Spotify. However, there are some ideas here in the community requesting the addition of this feature or related ones. Check it here:
If you want to, feel free to submit a brand new suggestion anytime...
In order to keep your listening activity private, you can also start a Private Session before listening to what you want to. Check this how-to support article to get more information about this feature.