Sorry, but many of us put Neosporin in chickens eyes without a problem, especially if it is an unopened tube or has been used with sterile technique. Terramycin is an eye ointment, but Neosporin ophthalmic ointment only is available by prescription. If chicken owners couldn't use the Neosporin in their chicken's eyes in emergencies, then they would not be able to treat most of their injuries. Being an RN, I wouldn't recommend using Neosporin in human's eyes, but I think it is fine for chickens. Pharmacists have posted on here that OTC Neosporin is fine for chickens. Vetericyn eye gel is great, but many won't or can't spend $20 or more on something for a chicken.
Just because folks have been using it for eons doesn't make it good or right or even the best option. Folks have been using peroxide forever; now we know not to because it kills living tissue, too.
Anybody who has animals should have a first aid kit that's properly stocked. Doesn't mean they need to spend a ton, but they should have the basics to get started.
And I would put raw honey on anything {including in an eye} first.
Of course, feel free to feed or treat or house, etc, however you want. Folks have been doing *whatever* {feeding just cracked corn; feeding layer to chicks, heating coops with heat lamps, etc, etc, etc} for years and they've never had problems, either.