Many differences are quite easy to overcome. Moderate- and high-gravity-worlders, for instance, can live in a mid-to-low-gravity environment without much trouble, at least for a little while. Plant-men, humans, and slime-molds can share the same atmosphere. Stationary or slow creatures can use hover-lifts to get around. Even some normally-aquatic creatures may be able to get out-and-about, as long as the air is humid.
For those that require (or merely demand) full immersion in liquid, broiling temperatures, caustic air, or otherwise extreme environments, however, nothing short of a full environment suit will do... most places. Luckily, the motto of Space Station V is, This Place is Nice 'Cause We Built It Twice.
The motto, of course, is untrue. The station was actually built a dozen times, with more on the way; each replica holds the lowest common denominator for the comfortable survival of the maximum number of races. One station is full of water, another hundreds of degrees hotter, and still another filled with caustic air. However, each station is otherwise a perfect duplicate of the original... visually, anyway. The stations beam fully interactive holograms to the others; that way, a magma man can shake hands with a (holographic) water-dweller, and a low-gravity-worlder can carry on a cheerful conversation with a high-gravity-worlder. Ships are automatically routed; where required, transport ships carry passengers to the correct stations.
Shops, too, are duplicated between stations, though for a few shops that is simply not possible. Water-dwellers, for instance, are disgusted by the idea of ice cream, and the asbestos-laden magma-man clothing store has little relevance to humans. In those cases, the shops in other locations are only painted store-fronts; while you can look inside and see a magmom buying a cute asbestos solar-flare-hat for her hot daughter, you're looking "through" an otherwise blank wall. The room inside is used for maintenance or storage. Some stores compromise with alternate or holographic wares; or, on the flip side, high-traffic locations are "double-mapped", allowing increased seating without wasting space seating holograms, yet still allowing a merman to wave to his slime mold buddy.
As an added benefit, computer-generated holograms can fill a variety of roles, from a basic prerecorded shopping hologram to make shops seem busier than they may actually be, to visually replacing high-dollar items, so shops can look full without stocking useless items. Renting a basic information hologram is much cheaper than hiring and training a real person, and cuts down on the minimum-wage retail-worker drama. Blank walls can be filled with holographic panoramas, making the compressed space of a station feel much larger, while ever-changing scenery alleviates the boredom of what is essentially a modern version of those old airports.