I'm not a big fan of the current trend in some quarters to universalize Jewish holidays, calling Passover the "Festival of Freedom," for instance, and then trying to apply its lessons to, say, gays suffering under the yoke of modern academia. (Put a purple ribbon on your office doorframe, so the liberating protestors will know not to molest you.)
Passover is, in fact, the most Jewish-centric of our holidays. It's the holiday that commemorates when, under the pressure-cooker of a midnight escape, we became a people, a nation, rather than a rabble of slaves. It's a holiday where we leave tyranny for the - as yet undefined - servitude to God.
Part of the Haggadah - the script for the Passover Seder - I believe emphasizes this particularism:
It is told of Rabbi Eliezer, Rabbi Yehoshua, Rabbi Elazar ben Azaria, Rabbi Akiva, and Rabbi Tarfon, who were reclining at the Seder in B'nei Brak, and had spent the whole night telling the story of the Exodus...
The irony is that of the rabbis in the discussion, all but one are either converts or descended from converts. The other is a Levi, and tradition holds that the tribe of Levi didn't suffer under slavery the way that the rest of Israel did.
This means that of the rabbis discussing the law, about none of them actually had ancestors who were slaves. The fact that we read this story on Passover in significant, because it implies that it's the Passover Story that defines us as a people. By accepting this story, the Passover story, as their own, they became a part of the people. Not simply an act of faith, or a belief in the universality of God, but an act of identification with the Jewish people was necessary for them to be accepted. Once they were accepted, they became some of our greatest rabbis. (The similarity between conversion to Judaism and immigration to America is striking, but a topic for another day.)
The question here isn't one of conversion per se, something better dealt with in Ruth,/I>, but one of applicability. Outside of Judaism, the Passover Story is someone else's, not applicable at all. Inside of Judaism, the Passover Story is their own. So much so, that it's their discussion that we study Seder night.
Happy Passover!