The tabloid's obsession with Harry and Meghan made it impossible for them to remain a part of the royal family. The public scrutiny—and at times, prejudice—directed at the couple meant that they needed to leave their royal status behind. They may know that means a loss of privileges, but it can hardly be suggested that requiring security is a privilege.
No, average celebrities do not receive public funding for security, but the average celebrity is not also a member of a national government. Through their royal ties, Harry and Meghan's status is different than most celebrities, and therefore should be treated differently.