I'll ride if rain is in the forecast, but not if it's actually raining when I leave home. I've been caught in rain several times the past couple of years. Unless the wind is blowing dangerously I just keep riding.
Usually I'll choose a route where traffic won't be a problem. I'm confident in my tires so I don't worry about that. With cantilever rim brakes I'm much more cautious and do plenty of advance braking to squeegee off the water and road crud. I wear clear safety glasses with foam seals around the eye sockets. A few times without glasses hard rain or debris would get in my eyes. Just a momentary distraction from blinking away the sting can be dangerous.
The main deterrent? Laundry. Especially the shoes. A couple of times this spring I had to pre-soak everything, especially my shoes, in a bucket to get the mud off before putting 'em in the machine. I'll probably put fenders back on one bike so it'll be less messy.