I think this is normal. My dd3 will be turning three in June. She has always been a super open/happy with anyone kid. She would go to anyone as a baby/young toddler. She was fine with me leaving. She was fine with Dad, with Grammy, with Auntie, with high school sitters, with the neighbor.
Well.... the last few months she has been clinging to my leg, acting shy around people we've known all her life, etc. It is a drag but it is just a phase. My dd1 and dd2 both did this and got out of it again. I honestly don't remember exactly when... I don't think it was too long though - as they both went to co-op preschool at just a couple of months (for dd1) and a couple of weeks (for dd2) after turning three. Both were totally fine. So it should pass fairly quickly.
I seem to remember something about equilibrium/disequilibrium in children running in six month cycles.
When my dd3 does it (acts shy, clingy, etc), it seems real but not terrifying if you kwim. I just try to act as though everything is fine (easy because it is) but don't force her to hug someone or be somewhere she doesn't seem to want to. She warms up with time. If she wants to hang on my leg while dd1's friend's mom is here talking to me, no biggie. She doesn't scream though so it is not really a problem for anyone but me (if I need/want to move around or tire of carrying her).
But I can imagine it would be harder with two! Try to hang in there; they'll grow out of it.