Not everyone caught the cutsies when Dez Bryant posted a pic of his supposed new pet monkey -- several animal organizations are FURIOUS ... claiming the move is downright "irresponsible."
The monkey in the middle is "Dallas Bryant" -- who Dez snuggled up with earlier this week and called, "My new best friend." Several reports say he "adopted" the animal.
But it's a HUUUUGE mistake according to multiple animal groups ... groups begging the NFL star to give the monkey to an animal sanctuary as soon as possible.
One of the critics is April Truitt -- co-founder of the North American Primate Sanctuary Alliance -- who tells us, "A baby capuchin monkey is completely irresponsible to have."
"This animal can easily live 30 to 40 years of its life. I guarantee you it won’t be in his possession that long. Instead he will begging someone like me to take this animal off his hands. It’s inevitable."
"I guarantee you this was an expensive purchase and he will live to regret it I guarantee you."
We also spoke with Dr. Ian Robinson -- V.P. of the International Fund for Animal Welfare -- who says, "Having a monkey as a pet is a huge commitment. Appealing cuddly babies turn into troublesome 'teenagers’ and aggressive adults."
As for Bryant -- he has NOT clarified if he plans to keep the animal as a pet ... but we're told NAPSA plans to reach out to him to try and talk him out of it.
'Cause no one wants Dez's monkey to end up like Justin Bieber's ...