From poking around and testing various pieces of headgear such as the welding helmet, some cowboy hats
and eyeglasses I've noticed what would seem to be a discrepancy in design. Depending on what headgear you
have equipped it may or may not ever take any damage. For instance the Sheriff's Hat will never take any
damage, or the welders helmet for that matter. The Rattan Cowboy hat will. Eyewear, from what I can tell,
is also indestructible.

Inconsistent design or intentional ? Anyone care to weigh in?

Another victim of near constant glitched game design maybe. I love New Vegas but its got so many glitches its not even funny. Thats just the way of things, certain clothing and guns are glitched and never seem to degrade. In my game This Machine never degrades past like 80 or 90 percent of its max health.

Maybe they figured it didn't matter? All of the items you mentioned have either 0 or 1 DT. I guess with the Four Eyes perk, if glasses never break it makes that pretty much a no-brainer perk since you find a pair of glasses like 5 minutes into the game if I remember correctly. But since they have such low DT, maybe they figured "who cares?". The other possibility is that you're not really taking many headshots, if everything's constantly attacking your body the headgear won't wear down.

Not that simple I'm afraid. I've swapped out headgear in the middle of using myself as a human target, letting vipers and bighorners tear me to shreds. The results were
pretty standard. The Rattan Cowboy hat, among others will degrade over time. Sheriff's Hat and welders helmet (DT 2) never takes any.

It's just like SOOOOOOOOOO much other stuff in this game. It makes no sense.

It degrades past that point in my game, but than not all bugs and glitches exist across every platform.

The problem is the equipment slots that the head-wear uses. There are Head, Hair, Headband, Hat, and Eyeglasses slots. It seems only head-wear that uses the hair slot loses durability.

Ah, I checked the wiki and it said this glitch was common with 360 players. What platform are you on?

Meh, carried from FO3 anyways. And it mostly happen to DT- headgear. As for Helm, sometime you are just lucky enough to not get head shotted.

From my personal testing, I can confirm this as well. Only an item using a hair slot will take damage.

Yeah I've noticed the Glasses will stay in durability but the helmets won't, but I've also noticed NPC's don't seem to want to repair glasses at all so maybe having them not break is a good thing.

Thats nothing.
Yesterday I bought T45d suit from Hover Dam quartermaster, almost broken. Next time I checked it in my inventory it had full health. So yeah lots of glitches.

This is a common problem. Most of the time if the vendor has two of an item and you buy the cheaper one it has full condition but only costs the price of a severely damaged item. Sometimes two items will appear as only one and when you buy one of them it will appear at full health in you inventory.

So is boones beret it does not damage

Common misconception. The actual bug is a little more specific, however. If you go to a vendor, that stocks two of an item, of different quality. Buying the lower priced one, will get you the higher priced one. Sell that one back to the vendor, and repeat the process, and you'll get yourself the fully repaired one (that is not on sale). This gets more complicated when the vendor has more than two, especially if they vary in condition; the item you get will be dependent on the order of the items as listed in the vendor's item list. Hope that helps