Hey, welcome to the 'moors!
First off, as others have said, it's more of a server thing. Brandywine is hands down the most populated server. While that can be good for lots of action, it comes with a price. Raids tend to fill up fast, leaving a lot of people waiting to get in. It really is, as you've suspected, a supply and demand thing. Since raid leaders can get the exact raid composition they want due to having so many creeps to choose from, they can be choosier on how many wargs they'll let in.
Sadly, current Brandywine raid leaders don't bother with waiting lists. Six years ago when my warg was literally green (they used the green-dot/blue-dot/red-dot system back then), I remember using /beg emotes while I waited for the chance to join a raid. (You didn't get infamy for PvE quests back then. There was only one way for a noobie to rank!) The leaders would do the same old, "PST with rank and class", but they were kind enough to keep a waiting list. That way, when people left, they could invite others. Many raid leaders were kind enough to let in a few greenies (but only a few). It seems raid leaders and their assists these days have lost the fine art of pen and paper list management.
Still, since you are a warg, you have other alternatives. Don't feel bad about only getting into warg packs. Warg packs rock! Perhaps other creeps see us as xenophobic, but the fact that wargs are fed scraps from the raids is precisely why we stick so tightly together. Back when I was on Brandywine, most of my ranks came more from warg packs (in fact, I'd call many of them warg RAIDS) than they did from mixed creep raids. Of course, virtually every warg was in Savage Fangs back then, and we ran packs round the clock. In the earliest days of Savage Fangs, and it's predecessor, Feral, we mostly camped rez circles and GV. The infamy came in slowly, but steadily. Eventually, there came a few updates where wargs could go head-to-head with freep raids. Those days might yet come again, so hang in there. You'll know they've hit when freeps start complaining on the forums that wargs are OP again.
I'd recommend you either get into a warg tribe, or start one if you can't find one. Invite every last warg on the server, and start running regular packs. All a warg needs to pull even a bit of weight in a pack is enhanced stealth, making warg packs the most inclusive of all groups and raids. There's nothing like the camaraderie of wargs to ease pain of ranking the slow way.
And whatever you do, don't scout for free. You deserve infamy for your work. Don't let those raid leaders abuse your stealth. (At least now you get credit anywhere on the map if you're in a raid. In the old days in a raid, a warg had to be in range of the kills for credit. Scouting really stank back then. You had to be careful that the raid leader didn't forget about you, or just flat out abuse your willingness to scout.)
Of course, you could always roll a defiler or warleader, but they're just so UGLY. (No offense to all the defilers and warleaders who have kept me alive over the years.) Enjoy your rich coat of fluffy fur.
Welcome to the fraternity of wargs.
[B][COLOR=#ffff00]Silverbullets [/COLOR]- Rank 9 Warg, Landroval[/B]