You can turn the question around: Are Father's Day wishes from regular people like you and me meaningful beyond self-promotion? Maybe, maybe not. I'm sure some people mean it sincerely and some just post them to get likes. This is no different with a celebrity. At its core, social media is just self promotion no matter who you are.
We all look up to role models for an example to follow and celebrities are very well promoted. Father's Day wishes should be personal and meaningful for the father and child but we can still learn from other examples around us. There should be a positive tone for a Father's Day wish that can be shared regardless of who it promotes.
While some father's day wishes may seem like an act of self-promotion, I honestly believe that most celebrities are honoring their fathers in a loving, meaningful way. It's ridiculous to think that there may be some ulterior motive beyond the well wishes. We need to remember that celebrities are people, too.
Every holiday, social networks are aflame with well-wishes and celebratory posts. Father's Day is no exception, and celebrities turned out in droves to create posts that talk about the holiday. In my opinion, this is just a PR move: it enables celebrities to take advantage of trending events and get the spotlight turned back on them.