This is definitely true for dogs/canids, eye contact is a signal of dominance and/or aggression. It’s common advice to soften your glance if you’re approaching an unfamiliar or potentially aggressive dog. It’s also helpful to make more direct eye contact when establishing you’re in charge when training them.

I’ve also noticed with many birds that they prefer indirect attention. This includes not just eye contact, but pointing a camera (or really anything) in their direction. Which unfortunately means I have very little photographic evidence of the many times I’ve had birds just hanging around being pleasant companions for a while.