I’ve never heard of an airline that won’t allow a personal item (mine — which I’ve taken on El Al and other airlines — is my tallis bag, which in addition to tallis and tefillin contains seforim and an iPad). If it’s a normal size, I doubt if there would be a problem, but if your personal item is as big as everyone else’s carry on, or if you’re struggling to carry it because of its weight…
Incidentally, Delta has no weight limit on your carry on. I’ve had another airline weigh my carry on just to make sure it wasn’t way over weight (it was maybe 20% over, but that was OK with them).