Do I really need bulb grease when changing low-beam or high-beam?
What you are referring to is dielectric grease. It doesn't conduct electricity so it is safe to use on electrical connectors.
Modern vehicle assembly lines don't grease bulbs because the rubber seals are sufficient at keeping moisture out, the electrical connection can be made more reliably.
Having said that, if the rubber isn't sealing properly, the grease may help with that and will prevent corrosion on the terminals.
Getting grease or any other contaminant on the glass part of bulbs can shorten the working life of the bulb, its best to wear gloves to prevent skin oils from getting on there.
If the terminals are corroded, remove corrosion with a wire brush and apply grease, otherwise leave it.
No, you don't "really need" it. However, the purpose of the grease is to keep out moisture that can degrade the connection and the bulb's performance. So if you see any signs of corrosion when you remove the old bulb, I would say that it would be a very good idea to clean the socket well and use some grease.
In my, limited, experience the bulbs that tend to need it the most are the tail lights, the license plate light, and the side markers.