How can an Orthodox Jew, Reform Jew and a Secular (non-religious) Jew live in the same apartment on Shabbat?

To the Orthodox Jew, those not living in obedience to Torah are 'outside.' That is where the term 'Gentile' is derived. It is the place where the 'dogs' live and wait for bits of wisdom like leftover food, just outside of the divine feast where the obedient enjoy God's full bounty. That means that there would need to be 'common' areas that are considered just outside the living space where the Torah of Shabbat is being observed and areas where the others agree not to enter during Shabbat, unless they agree to the observances themselves. This would actually help the Orthodox Jew because it would make the two others the required witnesses to their proper observance, (Deuteronomy 19:15), while also holding them accountable for entering any common area where forbidden work might become a temptation. In this sense, the two others are performing a type of mitzvah, even while they go about their 'common' routine. This can all be done very creatively so that it is an enjoyment and not a burden upon anyone.

Because where a person resides is not related in any way to their religion or ethnicity.

Anyone may live where they please. There are no religious rules about this

This really sounds like the beginning of a joke, and I just wish I knew the punch line: "An orthodox Jew, a reform Jew, and a secular Jew walk into a bar together ... " What are you really getting at with your question?

Non Religious Jew

Why not? Im orthodox and I've spent shabbos with non orthodox people. They just have to make sure not to do anything muktza for me, like turning on the lights for me.

(note: you are misusing "secular" with respect to Jews -- in the normative practice among those I know, an Orthodox Jew can be also "secular" - it just means that he participates in the secular culture ...you probably should have said "un-affiliated")

An Orthodox rabbi I learn with dormed with a Muslim guy in College.

There is no problem as long as everyone respects everyone else and recognizes each other's needs.

Really -- the only accommodations are:

(1) on Saturday, the non-practicing roommates need to remember not to turn off lights in the bathroom and some hallway light

(2) the non-practicing roommates need to respect the Orthodox guy's food limitations and his dishes/ food prep utensils.
Either the apartment would have to go kosher -- or the Orthodox guy's gear would have to be separate.

I have gone on two-week long campouts with friends that were of all different religious-cultural origins and practices.
I brought the pots and pans and we kept a vegetarian camp.

Fiddler on the Roof had a similar theme...In the end, everyone has to compromise

They each follow their own rules to the best of their conscience and leave the others to theirs.

Sure, why not?