imported post
Ok to settle the VA aspect, here is the relevant statute that states that written communication is sufficient.
§ 18.2-119. Trespass after having been forbidden to do so; penalties.
If any person without authority of law goes upon or remains upon the
lands, buildings or premises of another, or any portion or area
thereof, after having been forbidden to do so, either orally or in
writing, by the owner, lessee, custodian or other person lawfully in
charge thereof, or after having been forbidden to do so by a sign or
signs posted by such persons or by the holder of any easement or
other right-of-way authorized by the instrument creating such
interest to post such signs on such lands, structures, premises or
portion or area thereof at a place or places where it or they may be
reasonably seen, or if any person, whether he is the owner, tenant or
otherwise entitled to the use of such land, building or premises,
goes upon, or remains upon such land, building or premises after
having been prohibited from doing so by a court of competent
jurisdiction by an order issued pursuant to §§ 16.1-253, 16.1-253.1,
16.1-253.4, 16.1-278.2 through 16.1-278.6, 16.1-278.8, 16.1-278.14,
16.1-278.15, 16.1-279.1, 19.2-152.8, 19.2-152.9 or § 19.2-152.10 or
an ex parte order issued pursuant to § 20-103, and after having been
served with such order, he shall be guilty of a Class 1 misdemeanor.
This section shall not be construed to affect in any way the
provisions of §§ 18.2-132 through 18.2-136.
As for Washington, I couldn't find anything similar. So I'm holding to my theory that because signage doesn't hold any weight in trespassing someone from their premises, they are being green and not wasting plastic posting worthless signs.
So, all things considered, I would not be shocked or surprised in the least if Ikea has a no guns policy and they can consequently ask people to leave for it. That is part of the joys of this free nation and our (dwindling) property rights.