You don't miss out at all on job/race specific gear if your questing in another battlefront (Racial pairing). Any PQ's you complete and gain loot for always have an item you can use in the bag. It may not be better than what you have depending on the Chapter PQ your doing, but generally they are nice items.
Influence rewards are always job specific, so no matter where your collecting the rewards they will apply to you. Scenarios seem to drop fairly even amounts of gear for all jobs. Bear in mind, that doesn't mean you won't see your job drop in every one, just that it balances out.
Random world drops seem to me at a glance to favour the races who's lands your fighting in, but that would make sense to me I guess. It is still OB however, and it may be more even in release.
Also, unless your doing lots and lots of scenarios, or your really grinding the PQ's, you'll more than likely need to do more than just your own racial quests, at least in tier 2. While there are a mountain of quests available, its doubtful you will get enough xp to hit 20 without moving around a bit.
Morgrim - Ironclaw Server
Rank 40, Renown Rank 31
Immortal Guard Guild
Loaar - Retired
Galka, Pheonix, Serene LS
RDM 75 / PUP 75 / NIN 75