J.W.
Yes! Mine was that way by 3 months old. The pediatrician said it was young to start but still normal. On the other hand I've known other babies who were smart, and grew up just fine and never had it. So apparently the range of "normal" is very broad.
One thing that helped was to show friendship in front of the baby - like an exaggerated hello and warm embrace, then talking. My daughter would then relax and be more accepting of this stranger. I had to tell the person not to even look at her at first until the baby had time to assess this new person, and accept her.
Still, she did not tolerate being left with other people, even other family members like her aunt. She could cry for 8 hours straight not taking a bottle, when I had to leave her (I was having a non-elective surgery).
So, I guess I am not the best one to give a complete solution, but the show of friendship may help.