Among my close friends, I know Canadian, Israeli, and Australian dual-citizens.
I've never heard of having to "renounce all other allegiances". (Note: it's entirely possible that there is some obscure method of obtaining US citizenship that requires it; but that's not the norm.)
Additionally, my brother became a Canadian citizen (born U.S.), and again had no problems; Canada didn't care about his U.S. citizenship, and the U.S. doesn't care about his Canadian citizenship. He could officially renounce his U.S. citizenship by walking into a consulate and doing so, but there's no up-side to it.
If America would get a draft again, could a dual citizen be drafted?
If that were to happen, there would definitely be an upside to renunciation. ;-)
In general different countries have (very) different sets of rules, see e.g. http://en.wikipedia.org/wiki/Multiple_citizenship
Also if you volunteer (as opposed to being conscripted) for military duty in your non-US nations then the US can kick up a fuss.
But basically if you're a dual citizen with a nation friendly to the US then you really have nothing to worry about.
As far as I know, Uncle Sam only gets pissed when you acquire another citizenship after you are already an American (either by birth or by naturalization). Even so, there are provisions in the law that account for the situation when a second citizenship is bestowed upon you without you actively requesting it (some countries do that automatically when you marry one of their citizens)
But it doesn't mean that you actually renounce citizenship of your home country.
Well from the linked Wikipedia page it does mean that you actually renounce citizenship. It's pretty clear in having you state that is the case. If you actually don't then you are lying.
>"I hereby declare, on oath, that I absolutely and entirely renounce and abjure all allegiance and fidelity to any foreign prince, potentate, state, or sovereignty of whom or which I have heretofore been a subject or citizen;
For example if your former country required you to submit a form renouncing citizenship / sovereignty then taking the Oath and not having done that seems a highly dishonourable thing to do (ie IMO you're lying).
From that Oath (granted my first viewing of it in full) it seems that no truthful person could become a citizen of both America and some other place unless they were American first and no longer made that Oath on any occasion.
Uruguayan law says that even if you renounce your uruguayan citizenship, you still keep it. I think this was put in place exactly because lots of Uruguayans were leaving for the USA (lots of Uruguayans is something like 50).