For context, I've only seen the first film, and only all the way through at a social event.
When Neo is unplugged, he's leaving a sterile or at least very isolated environment, getting dunked in sketchy standing water, and being exposed to other people for the first time in his life. When you increase the size of your real life social group dramatically, even if you have a completely healthy immune system, you're likely to catch something, a la fresher's flu or con plague. Why doesn't this happen to him?