To answer your original question, it takes a group to fail. Not one individual with lower then desired gear. There are a very few minimums that you need to meet to be heroic ready and they can all be done in easy to acquire blue (and sometimes green) items. The rest is how you use your skills. Granted, things get difficult with someone in a 5 man not pulling their weight, you can still plan and conform your play to accommodate the weak point. Certainly there are some positions that are more noticeable when they are weak, but the best way to protect yourself from situations like that is to learn some common things about other classes. Typically when the tank is going down and is reasonably geared, people's gut reaction is that the healer is failing but that's not always the case. Look at the activities of the dps: Is there a hunter dishing out 3.6k, consistently going after multiple targets to pad his dps, and busting FD every time it's up? He's probably dropping threat to the healer who is getting interrupted or killed 30-40 yards away from the tank. There are many scenarios like this and the best protection you can afford yourself is to learn a little bit about the different classes and be more situationally aware of "bad situations."
The fact that you are being self conscious about this is a good thing. If you see something in a group that you don't like after you learn some things, call it out. If the group doesn't change and you still get the vibe, drop group. It's not worth your time or effort to make yourself feel bad when it's not your issue. It's certainly not worth the rep bill. GL!
Execute for show, tank for dough.