Is it safe to eat raw green beans which have been in brine at room temperature

It rather depends on the temperature of the room. Where I live, in the summer it gets hot and humid, and they shouldn't be out on the counter during the day, or they ferment. In winter (like spring in the northern US, 45-70 farenheit) they can be out for two days with no problem.

My recommendation would be to soak overnight for morning use, or to soak during the day for evening use. It also helps to change the water every few hours, though this isn't critical. If you refrigerate them with the water, you get an extra half-day. Refrigerating drained gets another day or so.

Either way, they should always be shaded, never in direct sunlight.

If they do spoil, you'll know, as they'll have a sour/yeasty smell to them.

Botulism thrives in high-moisture, low-acidity, low-salinity, anaerobic environments at between 50 and 130 degrees.

In your refridgerator pickles, you're:

1. keeping cold
2. adding acid
3. adding salt

All of which should at least prevent the botulism from reproducing in great enough numbers to be toxic, if not outright killing it.

That's not to say nothing nasty can grow in refrigerator pickles — you're likely safe from botulism, however.