I think generally handling a reptile is fine, I definitely don’t try to catch every reptile I come across, but from time to time I’ll pick some one up, especially if it’s a species I’ve never encountered before. I don’t think the short-term stress from being captured is likely to have any long-term effect on the animal, and unless you’re capturing reptiles back-to-back I think the odds of disease transmission between individuals is fairly low. Reptiles living near each other are likely to encounter the same pathogens in their environment anyway. Road-cruising for snakes over a large area is a different matter, but the benefit of moving the snake off the road probably outweighs the risk of passing along a disease. Fortunately snake fungal disease hasn’t hit my area yet, that may change when and if it does.
I do think it’s important to know how to handle a reptile safely, but I think in most scenarios the greatest risk to the animal is going to come from people causing lizards to drop their tails, because of the health impact others have mentioned. I see a lot of photos on here of people dangling fence lizards and anoles by their tails, and I’m astonished the lizards in the photos aren’t dropping them in those scenarios. I usually try to leave a comment on those observations advising against holding lizards that way. Unfortunately the only way most people are going to learn where to grab a lizard to cause it to not tail-drop is through experience, I certainly caused lots of lizards to lose their tails when I was a kid. It’s tricky to get that reflex to release the grab if it’s too far down the body.