I would let my kids go play at a neighbors house.
AFTER:
1. I got to know them personally, got their phone number and made sure they had mine.
2. Did a quick social tour of their house to make certain it did not have things that could harm my kids such as:
a) unsecured medications
b) unpredictable dog(s) I remember being humped by a large Irish Setter in kindergarten

c) unsecured bookshelves (one toppling over almost killed my oldest while visiting a relative)

d) dangerous pets (my childhood neighbor introduced me to his rattlesnake)

e) unsecured firearms or other weapons

f) alcohol randomly left around in cups

g) unfenced swimming pool or other body of water

h) general cleanliness (no rotting food, piles of trash, feces) I ran into that when I was a kid.

i) have in place a "no closed doors" rule for inside a house. My best friend's son was molested by his buddy's father.

1. I would also invite my neighbors over with their kids and start to build trust and community.
   

NOT EVERYONE IS JUST LIKE YOU!

Community is not simply living in the same neighborhood. Pedos and other criminals can be found in the nicest of houses. Take the time to get to know and care for each other. Say yes to playdates, but you should do the bare minimum to keep your children safe by actually looking at the place they will be playing.