THey are as real as all other psychics, which is to say (in my opinion) not real at all.
Being somewhat unusal, I know five pairs of identical twins. None of them have any special abilities of gaining knowledge with regards to their other, uh, half.
Ah, that would be the fallacy of selective remembering.
Your twins remember the occasional times when they knew “exactly what is going on with each other”, but forget the vastly larger number of times when they there was no apparent psychic connection. How many times did one twin not sense when the other was experiencing something significant? How many times did a twin think she was sensing something that turned out wrong? Those experiences tend to be forgotten or not considered at all, and the “connections” remembered and reinforced (in the person’s mind) over time.
It’s no mystery that they can occasionally predict each other’s behaviour - they were likely very close when growing up and thoroughly learned each others personalities and behaviours. I’d be surprised if there wasn’t an occasional coincidence when one appeared to know exactly what was going on with the other.