The guy who "taught" me to use a saw didn't use any safety gear. Even then I used safety glasses, but that was it. No hearing protection or anything else. This was the same guy who thought "tuning" a saw was leaning it out as far as you dare, and when it burned up, well that was just how long a saw lasted. If a saw lasted more than one firewood season, that was a damned good saw! Very glad I've learned beyond what he knew.
What I wear depends on what I'm doing.
If I'm just starting/revving saw, only hearing protection.
If I'm cutting anything, safety glasses and hearing protection. If an electric saw, sometimes not the hearing protection, but even then that high pitched whine is loud enough to be damaging if used for a length of time.
Any.running of a saw with unsure footing, or if I'm tired, or cutting anything awkward, or if it's nasty and I want more weather protection, or if I have to kneel on anything and want more padding, out come the chaps.
I don't do any tree work, just a firewood cutter, haven't felled a tree in years, and just this week bought a hardhat for storm cleanup.
Edit: Gloves occasionally, mostly that's to protect my hands from whatever I'm handling when I'm not cutting, though they do add a level of vibration protection too.
Steel toed shoes are my standard footwear. Even my business casual office day job shoes are safety toe.