[PTTG]

Well, for a start, there's some kind of mars-adapted plant life (it probably needs sheltered, specially treated soil and some kind of water source, but it doesn't need a total artificial environment).

Water recycling is highly effective. Any losses are replaced by ices that are extracted as a by-product of hydrogen mining (in fact, fuel tanks may store water, then crack the hydrogen out and use that as reaction mass as needed).

Oxygen is in a similar boat. If you aren't thirsty, you can generally breath.

Food is more difficult. Hydroponics exist, but they are so bulky that you can't fit them in most mobile ships. Ships need to stock up on food frequently, and because of mass constraints, it's usually pretty bland.

Earth IS essential because "nutrient recycling" is the least efficient part of the life support cycle. If Earth was totally destroyed (by, for instance, a relitavistic attack), pretty much everyone else would eventually starve as rare nutrients disappeared. In theory, those biosphere services could be replaced, but the state of the art isn't there yet. Mars is the closest to providing full life support.

Besides the essentials, Earth is where almost any food that isn't algal paste comes from.

The Moon and Mars had more traffic than the rest of the solar system. They couldn't even keep the flu out, even with the enforced 30-day quarantine.