This can be accomplished with or without CBSubs. The first option with CBSubs is to create a dummy plan that no one is able to subscribe to. You then used cbsubs fields tabs protection to protect a tab based off view subscription and select that dummy plan ensuring owner and moderators are not also restricted (user detailed mode). This would then limit display to moderators and profile owner as no one can obtain the dummy plan.

Another option is to move the tab to a not shown on profile position. Once done use a delimiter field and IF based substitutions (see signature for tutorials) to limit who can see the substituted fields content. This would hide the content, but not the tab however.