Facebook seems to constantly deal with issues that have to do with privacy, many of which are specifically its own fault. Its privacy mess-ups could ultimately cost the company a record FTC fine in the billion dollar range. Facebook recently warned popular health apps that use its API to be sure they have legal justification for sharing personal data with Facebook, seemingly indicating that the data major health apps are sharing with it, is data it hasn't asked for. Facebook is now caught up in another privacy issue.
This one has to do with the social network calling on users to secure their accounts with a phone number for additional two-factor authentication protection. The problem for users is that when Facebook associates the phone number with their accounts, the user's profiles are linked with the phone numbers. That linking allows anyone to search for a Facebook profile using the phone number.
Facebook offers no way to opt out of that phone number search feature. It has been forced to admit that it used the phone numbers to target ads at its users. For years Facebook had claimed that the phone numbers were only used for authentication. Don't confuse what's going on here with hiding your phone number from your profile, that still won't prevent people from searching for you using your number.
The good news is that while you can't opt out, you can control who can look up your profile using your phone number. The default setting is "everyone", but you can change that to "friends of friends" or just "friends." Facebook says that the setting is not new and that it has always been there and applies to any phone numbers you added to the profile. Facebook also maintains that the setting isn't specific to any feature.