I recently moved into a new home, and I was replacing a light bulb when I found this after removing the glass cover. 
Now, I don't know much about codes and regulations, and I'm new to working on my own home, but this screams "fire hazard" to me, so I want more input before I install a bulb and continue to use this. Is this okay to have insulation next to something that gets hot? Why is/isn't it?
This is a good question - seeing some insulation in your light fixture can be a bit of a shock.
Think about it, though. Those incandescent bulbs are inside a glass globe. One of the best features of an incandescent bulb is its ability to turn electricity into heat. What's that heat going to do when it's trapped inside the globe - it's going to melt the wiring or catch the ceiling on fire.
The silver reflective foil reflects heat and light away from the ceiling material and the insulation helps keep whatever heat doesn't get reflected from moving through and melting your wire's insulation which could result in a short and the whole house getting really hot and a visit from the fire department.
Putting the insulation inside a light fixture is a very bad idea. This was probably invented by some US electricians/contractors/light fixture makers that had absolutely zero idea about heat transfer.
Think about this first. The US construction code requires the ceiling space around high-heat-generating fixtures to be cleared, i.e. no insulation on top of ceiling lights, unless the fixtures have a high heat-resistant rate. There is a reason for it. The temperature increases when the heat concentrates in a small space. Heat from light bulb needs to be dissipated into the air to prevent burning/melting. Then some people put insulation both on top and inside the fixtures, adjacent to bulbs. That becomes a perfect heat trap. I’ve seen melted bulb bases, burned wires, and melted fiberglass thanks to that.
There is sadly a lot of misuses of batt insulation by homeowners/contractors. In this case, it becomes an obstacle when repairing the fixtures or replacing the bulbs. In construction, adding obstacles means adding risks. Moreover, this is considered a mod. Adding mods to light fixtures means taking all responsibility for any potential damage.
Inhaling fiberglass is a common cause of lung problems in construction. And with this insulation stick around, you might need to wear face-mask and eye-protection for just replacing a bulb.
What to do instead: use low-heat bulbs, use correct-sized bulbs, keep the space on top of the fixtures cleared, choose a well-designed fixture.
