Highrise doesn't have one switch that makes your whole account private. Instead, you choose who sees each part of your profile in Edit Profile > Privacy Settings: your online status, the room you're in, your country, your posts, and your Wishlist.
Where are my privacy settings?
Open your profile and tap the more button in the top right.
Tap Edit Profile.
Scroll to Privacy Settings and change what you want.
Tap Save.
What does each setting do?
Online Status: who can see when you're online. Choose Everyone, Friends, or Hidden.
Room You're In: who can see which room you're in and follow you there. Choose Everyone, Friends, or Hidden.
Country: shows or hides your country flag. See How do I change or hide the country flag on my profile?
Posts: turn on Private Posts so only people you approve can see your posts. Your existing followers keep access.
Wishlist: turn on Private Wishlist to hide the items on your Wishlist.
Friends are players you follow who also follow you back.
What happens when I make my posts private?
New followers have to send you a follow request, and you approve or ignore it.
Players who don't follow you can't see your posts.
Your posts are removed from other players' saved posts.
If you switch back to public, any follow requests still waiting are accepted automatically. Each post keeps the visibility it had when you posted it, so a post made while private stays private. To make it public, post it again.
Can I hide my followers or friend counts?
No. Your Friends, Followers, and Following counts are always shown on your profile. You can remove a follower: open your followers list, tap the remove button next to their name, then tap Remove to confirm. They aren't told they were removed.
If someone is bothering you, block them. You can see and undo blocks in Settings > Privacy > Blocked Users. See How do I block or mute someone?
I'm under 18. Are my settings different?
If you were under 18 when you signed up, your profile starts more private: posts are private, your online status and the room you're in are shown to friends only, and your country flag is hidden. You can review these at any time in Edit Profile.
What about messages and room access?
There's no setting that limits who can send you a message request, but requests wait in a separate list until you reply. See What are Message Requests in my Inbox? To control who can enter your Rooms, see How do I change who can enter my Room?