I've found that an early rush is only advantageous if one or more of the following are met:
Sorry, but I'm going to disagree with you on all of these!
A) You have a good early UU civ. Persian Immortals are my personal favorite and you can begin pumping them after just a few turns. Roman Praetorians are popular as well, though I wouldn't consider that an "early" rush since Iron would already be in the picture (by which time everyone has made friends).
An early UU is absolutely not necessary for a successful early rush. Generic Axemen or Chariots will more than suffice. I'll grant that an early UU makes an early rush more attractive--even imperative in order to leverage one of the main benefits of playing as that civ--but it is not a requirement. You simply need to build a few more units--this is where chopping and whipping come into play.
B) Your closest neighbor is extremely close. The only time I've had luck with rushing is if the target's capitol was only ~10-15 tiles from mine. Otherwise the turns wasted getting there gives them more time to build defenders, not to mention maintenance costs will tend to stifle your research. This is pretty map dependent, since obviously there's no need to rush if you're relatively isolated with plenty of room for expansion.
I would tend to agree, except for the "extremely" part. If the target cities have other benefits--say, a holy city with a shrine, or just a lot of food and gold/gems/silver, say, then that can offset the maintenance costs you'll run into. If the opponent is distant and his cities offer few benefits, you can still gain a significant advantage by simply raiding his territory and stifling him--stealing workers, pillaging improvments, razing poorly-defended cities.
C) Your target has not already made friends. All the more reason to rush extremely early, before they have contacted other civs and founded religions. Easy way to tell is to look at the Foreign Advisor screen under the Glance statistics. How many civs have + relations with your target? If a lot, don't bother rushing them.[/QUOTE]
Worrying about this really depends upon your long-term strategy. If you plan on playing toward a domination win and being the biggest, baddest kid on the block, you won't be as worried about ticking off your first target's buddies, because they're likely going to be targets # 2, 3, and so on.
What you ideally want to do is to work the diplomatic angles so your other neighbours leave you alone while you war on another one. For example, in a recent game as JC of Rome, I had Ramesses and Justinian to my north, Wang Kon to my south. Ramesses built the Great Lighthouse, founded Buddhism, and built its shrine, making him an extremely attractive target. Justinian was his Buddhist bosom buddy. Wang Kon, on the other hand, founded Taoism (but did not build its shrine). Buddhism spread to my cities, but I waited for Taoism to do so before I chose a state religion. This ensured that Wang Kon was friendly (after several turns, literally) and left my southern border alone while I warred on Ramesses and Justinian, each in turn. Wang Kon also eventually fell to the Praet storm, but not until after I'd finished off my northern neighbours.