What can I say about Inflatable Travel Pillows? Most of which I think are disposable after one or two flights if you're lucky! I always see them in the trash! (Just don't expect a Crew member to blow it up for you --unsanitary!--)
I would suggest using our pillows but cover them with a pillow case. I travel with my own anyway. It comes in handy to cover my backpack if I fall asleep on a train or bus and don't want the pockets exposed. You could also put it in a plastic bag that bedsheets come in first with a pillowcasw over it. I've seen that on a couple of occaisions as well.
Blankets can be a health concern. If it's sealed in plastic you're pretty safe to assume it's been freshly drycleaned. Otherwise it may be recycled so simply refuse that. It should not happen but I'm sure it does...I think most Carriers now seal them in plastic as standard procedure.