It was a bright green pigment that contained the arsenic, from a compound of copper arsenite. Vivid chemical dyes were a new thing in the 19th Century, and all the rage. It wasn't just William Morris's wallpaper that used the green dyes, it was very common.
"That arsenic was poisonous was certainly not a secret; every Victorian home had a bit of the powder lying around for rats and mice, and people likely knew tales of the “inheritance powder” being used for murder. Yet they also applied arsenic cosmetics, gave their children toys painted with arsenic, wore dresses and hats dyed with arsenic, and ate meat dipped into it to keep away flies.
(I have a death certificate of one of my ancestors where the cause of death is "arsenic poisoning" but no mention of an enquiry, and I can find no sign of a coroner's report. Arsenic was so common that accidental deaths must have been frequent. )
Of course, very small regular doses of arsenic were taken by some middle-aged men. It made their hair shiny and thick, improved their skin, and gave them more stamina in important (to them) areas where they felt they were wilting. There is a detective story by Dorothy Sayers where a murderer had deflected suspicion by sharing his victim's poisoned meal, and surviving because he had been accustoming himself to arsenic for months beforehand. Lord Peter Whimsy noticed the luxuriant barnet and unmasked the villain.)
In some kind of disconnect, people believed that only by licking the walls would they get poisoned, or only by the green colors. In this way, it wasn’t too different from the radium cosmetics that took off in the mid-20th century, even while the potentially dangerous power of radiation was evident. Left untouched, Victorian wallpaper could still release flakes of arsenic into the air or produce arsenical gas when conditions were damp.
There is a parallel too with the use of asbestos. and luminous radioactive paint on the hands and numerals of clocks and watches.