Would a loaded cartridge ignite/explode when hit from the side or front by a bullet?
Maybe

Unfortunately, the correct answer is “it depends.” Small arms cartridges struck by small arms projectiles generally do not ignite – but they do sometimes.

The issue is quite important in the armed forces. If you come under enemy fire, the last thing you want is for a near miss to cause your own ammunition to explode. There has been formal research on the subject for decades. However, it can be quite difficult to prevent.

There are formal test protocols to assess the safety of new ammunition types, and they can involve munitions struck by a range of different “stimuli” from various distances, points of impact and angles. Depending on the exact set-up, the response can vary from 100% explosion to barely scratched.