Why was Boromir allowed to join the Fellowship?

[Formendacil]

The only problem with saying that there was a concern for Rivendell and Gondor's relationship is that there WAS no relationship between Rivendell and Gondor--when Boromir and Faramir had the vision, they had no idea where Imladris was, and though Denethor is able to tell them basically where it lies, it is clear that he is speaking of ancient lore--not correcting geopolitically-challenged sons. After all, the last time Gondor was properly involved with Rivendell in anything, there was still a King on the throne.

In the sense that both were opposed to Sauron and in desperate straits should he win, Gondor and Rivendell were certainly allies--but not in the sense that there was anything deliberate about this, especially on the side of Gondor which saw itself as alone against the world (save Rohan). Gandalf, it is true, was known in both, but I think it's fair to say he was already less-than-popular in Denethor's court.

Rather than the political reality, I think it comes down more to Gandalf and Elrond's assessment of Aragorn. Aragorn, we are told, is also going to Minas Tirith--if the Fellowship is about those only going with Frodo and the Ring, he should be out too. One could even argue that two parties leaving Rivendell in different directions for the southlands would have been good cover for the more important mission, but--and this is more my impression than something I have a direct quote handy for--it would seem that Gandalf thought that some Aragorn was better than no Aragorn on the trip.

And if you're going to take Aragorn, you should probably take Boromir then too. While that does have a political dimension (Boromir is, after Denethor, the one who will be most directly impacted by the return of the King and his support would mean the difference between a coronation and civil war), it's also courtesy--and I don't think courtesy for its own sake likely to be undervalued by either Gandalf or Elrond.