BuildCraft's Redstone Engines are slow, but I have always been taught that their one advantage is their inability to explode.
Is this true, or am I secretly in danger if I leave them on too long?
No, redstone engines don't explode in normal conditions (when are connected to something):
Redstone engines ... unlike Combustion engines, will never explode on running hot, except when not powering anything.
A single engine that is powering something cannot explode, period, even if the thing it is powering is doing nothing. However, it is technically possible to blow up a redstone engine if you have other engines pointing into it (daisy chaining power), even when it is powering something. You really do need to put effort into it to get it to explode.
This has changed, from the wiki:
Prior to BC3.7, redstone engine would explode if allowed to overheat. Being connected even to a single wooden pipe (even if leading nowhere) will allow it to run indefinitely without any risk of exploding.
So, a single wooden conductive pipe (even just a 'stub') is enough to prevent them from overheating and exploding. Thus, it's definitely worth considering a redstone engine any time that it'll be operating without much supervision (presumably through the use of a chunk loader), and the power demand is compatible.