I'm not saying that site is a master piece of work or that it holds the truth. I do however consider 20mW lasers dangerous and I advice to take safety serious. With all the watts around people seem to get sloppy on safety and push the limits of what they consider safe.
I'm not saying it's goggles or die, I've worked with a 5W Spectra Physics Millenia without the goggles for it. It was bolted to an optical table and the beam path shielded as recommended by the laser safety officer. It was a stationary setup, nothing was handled that came close to that beam.
Pointers however are different, just take a look at the sticky of Xoul in this section. In a professional situation Class 2 lasers are allowed for alignment, nothing more. Saying class 3A is safe is already stretching that up, but considering the small chance of eye damage that can be arguably justified.
So let me be perfectly clear: 20mW lasers are dangerous and 8mW lasers are dangerous too. Take the safety precautions applicable to a class 3b laser. I don't give a sh*t if anyone thinks I'm exaggerating, we're talking about laser safety here, not about your favorite flavour of lollipops.