I know the Gymnocalyciums like more shaded conditions than barrel cacti. However, I'd think a lot of them could handle it if introduced slowly enough. I've got one outdoors underneath a huge locust tree all day. With the sunlight being as intense as it is this time each year, perhaps it could be considered full sun even though it's in shade. I'd not move my Gymnocalycium into full, direct, intense sun now, but in a month perhaps when the summer solstice is passed a bit more. I guess it just depends on how intense the light is during the growing season. I'd say most cacti could technically be put in full sun, acclimated of course, any time of the year. I say that since, technically, full sun is seven hours of direct sunlight.

Early in the summer on a clear day, the direct sun is too intense for most cacti. On a cloudy day, they would likely be fine. I'd probably start acclimating them now. By the time they are acclimated they might be in just as much sun as they can handle. Hope this helps! :)

I am surprised to hear someone say they handle more shaded conditions. I live in Florida and the sun here is brutal. I get burned cactus all the time even desert species. My Gymnos on the other hand I keep in full blazing sun. They make flowers and if the flowers even have a hint of shade they won't open. I keep them blazing and the Flowers open up great and the plants themselves don't ever have a problem.