No. Thie distinction between "don't" and "can't" in this sentence is very subtle. Most English speakers would understand your meaning if you used either word. To say that nice people "don't" get the respect they deserve means that it just doesn't happen right now.. It may be possible for them to get respect, but for some reason they're not getting it at the moment and probably did not get respect in the past. "Can't" would imply that there's some actual impediment, something about them or their situation, that prevents them from getting respect. It also, in a very small way, implies that they want respect, and are trying to get it, and failing. In this context, it wouldn't really matter which word you used, a native speaker would understand the important message, which is that nice people are not getting respect.

I agree with nexus6. 'Don't' is correct. The writer is just saying that that's how the world is - he/she is stating the fact that this is what happens. Nice people don't get respect. If you changed it to 'can't', it would suggest that these people are trying to get respect but failing to do so. You could replace 'don't' with 'can't', but it would change the meaning, and I don't think that this is the meaning which the writer intended.