According to Joseph Meehan :

It is safe to use any device or lamp that does not have a polarized plug
(one with one prong larger than the other so it will only fit in the outlet
one way). Most devices with polarized plugs are also safe, but it may not
be easy to be sure. I would avoid using any polarized plug device in those
outlets. I would also suggest contacting the owner and having it fixed.

There is NO difference between a polarized plug fixture and a non-polarized
plug fixture other than the fact that the plug is polarized.

The only reason that bulb fixtures are polarized, is that a correctly
wired outlet puts the neutral (less hazardous) on the base shell - which
you might come in contact with while changing a bulb.

If the hot is on the base shell (from a reversed outlet), the base is
hot EVEN IF the light switch is off (because the switch switches the
neutral!).

In other words, with a correctly wired outlet (and non-defective fixture),
a polarized receptacle guarantees you can't electrocute yourself from
accidentally touching the base shell of the bulb or fixture, switched on
or not.

As a corrollary, with unpolarized fixtures, or, polarized fixtures
on an hot-neutral reversed outlet, you will want to consider unplugging
the fixture before changing the bulb. It's not necessary on a polarized
fixture on a correctly wired outlet.
--
Chris Lewis, Una confibula non set est
It's not just anyone who gets a Starship Cruiser class named after them.