I'm sure mormons prefer their adult friends be mormon and their children's friends be mormon as well...I'm thinking sleepovers, playdates and stuff.

Do/can mormons be close friends with never mo's? Is it frowned upon?

TBMs have recently been counseled against sleepovers. Sleepovers with nevermo's must be especially dangerous.

My girls have more nevermo friends than TBM friends and that is exactly the way it should be b/c TBMs are VERY small percentage (0.000001%?) of the population in our area

They can be friends, but being too close tends to be a stretch for them.

When I was growing up it was a big no-no. In fact, growing up in Wyoming when I was in 5th grade my parents made me stop being friends with the boy I had been like brothers with since kindergarten because he wasn't a mormon and it almost broke my heart. I could not date girls who were not mormons, and I could not even go to parties at homes that were not of mormon families. I'm sure it is still frowned upon by the leadership simply because the church is a cult and they discourage any outside commingling. After all, you can't maintain control over the flock if they are out socializing with the enemy!!!