Part one: First of all, if you were focusing on what you're saying, the question wouldn't even start regarding Selichos of Elul. You're praying for your life "like a slave pleads to his master." Would you really be talking to your friend in the middle of an impassioned plea to live another year, when your very life hangs in the balance?
Part two: As for Selichos of fast days: note that, unlike those of Elul, these are said between Shemoneh Esrei and Tachanun. The Gemara (Bava Metzia 59b) records a story that shows the power of not interrupting between these tefillos. In combining that with the pain he felt deep down from being excommunicated by Rabban Gamliel (long story), R' Elazar ultimately ended up killing the Nasi with his tefillos, albeit unintentionally. Recognizing these two powers, R' Elazar's wife (R' Gamliel's sister) kept distracting him between the two tefillos in order to prevent this from happening, but one time she slipped up, and R' Gamliel died as a result.
From here we see the power of not interrupting between Shemoneh Esrei and Tachanun. Selichos are of the same theme as Tachanun and thus aren't really an interruption (similar to saying Kaddish before Shemoneh Esrei of Maariv), but talking during that time certainly would be.