As Hazel's post and the more recent issue of the NE bat mortality shows, cross-contamination *IS* an issue. The question is how big an issue. Let me first say that I rarely wash my outer suit and other gear until it exceeds all standards of social norms
However, microorganisims can be both more fragile and more durable than you expect and I have no doubt that some species have been negatively impacted by the introduction of either new competitors or a change in the energy dynamics from the introduction of caver-borne "stuff". It is also possible that eggs from beetles and crickets can also be re-located by cavers so this isn't just a micro-bug discussion.
Also, contamination of wet systems is no less a concern, since the water could easily provide a very effecient method to widely distribute a new organisim throughout a drainage.
For me, it comes down to a ratio between how likely is a negative impact and how motivated I am to repeatedly clean gear. Am I visiting a cave with a known sensitive species or ecosystem? am I going in another nameless muddy tube? Being a biologist partial to bats If I were caving in the NE I would probably wear goodwill clothes and destroy them after each trip. For most caves most of the time I do nothing. I'm not saying that is a *proper* decision...just the one I make in the real vs academic world.