The Haste Helm doesnt have any armor tag, at least not on 6.9, which is what I'm playing.
Helmets, gloves, boots can be of light, medium, or heavy armor type. That doesnt mean they actually provide extra protection. That only means unless you have proficiency for this type of armor, you will get penalties if you wear this item. Mainly you'll be unable to cast spells on a spellcaster.
Some items give extra protection, but thats completely independent of the armor type of the item, and rings, amulets and cloaks can give extra protection, too (I dont think theres an amulet that actually does that though).
By the way, using a weapon for which you have no proficiency for results in no penalties. You just cant use the special attacks these items could provide. And get no proficiency bonus on the attack.