You can still dye them. Best to remove the waterproofing, and even though it's goretex there will be some, and then wash them in really, really hot water.
Get the dye bath hot, and then introduce the hot wet gaiters. Make sure that whatever dye bath you use is big enough to let the gaiters move easily in the liquid. (I use the biggest stock pots I can find, they come in sets, they're cheap and thin stainless steel with no sandwiched base. They're fine for liquid but no use for most cooking. I think mine cost somewhere around twenty quid, but on checking eBay, a set is now just under twenty eight pounds, and that's with delivery....
https://www.ebay.co.uk/itm/Set-of-4...594955?hash=item2809972fcb:g:LGsAAOSwKtlWomcU )
I know the dye is supposed to boil for ages, but I just turn the heat off, put the lid on, and just keep it sitting nice and hot. I stir it frequently and so far, it seems to have worked fine.
All dyes will look like they are running when first washed, but it's just the excess in the dye liquid. When you take the gaiters out, wash them in really hot water to remove that excess, and then rinse in several washes of cooler and cooler water. When it runs clear, you're done.
Be careful of splashes, the blasted stuff is hard to remove.
M