Can the UK royals disentangle their personal lives from their state obligations? It's a tough call - & I don't know that Obama even knows Meghan, nor Harry for that matter. Certainly the Trump would be offended if he didn't get an invite - he's normally offended anyway, I'm sure. But whether the royals would pointedly not invite the Trump may be a bridge too far.
Harry and Obama have been talking with each other since the Invicutus Games in Canada. Harry recently interviewed President Obama on his first job as an interviewer on radio. So, they have a relationship. THAT much irk Trump whose state visit has been postponed due to his dislike in Great Britain.