It's a power - draw heat issue. The socket can be used for anything that would normally screw into it. But being labeled CFL only they avoid the liability of someone burning down their business or home by over loading it. Most of these sockets are used by photographers and are covered or wrapped trapping even more heat.
I've used it with all types of bulbs. Its rated for a total of 300 watts--this is written on the side. PAR38 bulbs are too big for this, not enough room between the sockets to plug in more than two at a time. Otherwise it takes most anything with an E27 base.
I see no reason why a LED especially would not work in this device. Incandescent may get a bit hot, but it is built rather well and may hold up to them. It is made of a strong but semi flexible plastic (not the hard plastic found on many lamps or even the ceramic, that work with incandescent), and that may melt under the heat need from an incandescent. for short runs it would probably be fine but to be left on for hours you may have an issue.
I have used it for over a year with 4 of the Cree 60 watt equiv daylight 5000K led bulbs with no problems. Very pleased with this socket adapter. I just got a 2nd one and 4 more cree led bulbs for the other socket in the garage.