Since this is months old, I’ve already settled back then with the plugin “BuddyPress to WordPress Full Sync” which allows me to sync any arbitary xProfile fields to WordPress fields.
@imath I can confirm by now this works as expected when following your steps. Without being able to verify anymore what my problem was back then, I have a feeling this must have been related to validation as sometimes BuddyPress provides zero feedback when something was wrong. In my current WordPress version (5.8.3), the Twitter field is expected to be a simple username (not full URL / @), other fields like Instagram are expected to be the full URL. So perhaps the issue was that some fields didn’t match validation criteria, so BuddyPress just silently swallowed the input?
