I treat Twitter just like I treat all other media - you have to develop filters for processing the information and eliminating the noise. I don’t think there’s anything unusual about this, it’s just that Twitter is wide open, so without filters and a thick skin you’ll feel like you’re inundated with fools.
This is how the Internet works. It gives a voice to a lot of people who don’t have any sense of responsibility, as well as plenty of people who do. When I encounter idiots on Twitter, I just block them and move on. There’s no point in being upset about it.