They're not raiding without a priest, they're raiding with a shadow priest :)
But, if you are a good healer, you have nothing to worry about. There are so few healers out there compared to other classes that if you know what you're doing you will earn yourself a raid spot.
By the way, this was so last month :P Just messing with you, but you really are behind the times. For awhile now Paladins have been the raid healer of choice as no other healer can match their single target healing efficiency, plus bringing more than one paladin brings multiple buffs to the raid, whereas bringing more than one holy/disc priest doesn't bring anything extra in terms of buffs.
Next patch, Paladin healing is going to take a hit, so we'll see how things work out then. Personally I would much rather have seen priests and other healers get a buff rather than having Paladins be nerfed, a lot of paladins want to heal. If that frees me up to go Shadow, by all means make paladins great healers.
So yeah, if you can't find a raiding guild, the problem isn't that they're not taking healing priests, the problem is that you don't know how to heal. The only guilds not taking holy priests at all will be the hardest of the hardcore guilds who min/max to the extreme.