give out my business cards, which I always have on hand
This is said to be much safer than giving personal contact information, such as home phone number, to strangers.
The National Crime Prevention Council shares this webpage on
What To Teach Kids About Strangers.
if anyone we meet in person feels DS and I are a security threat or being inappropriate by being friendly, then they have some underlying issues, because we are so obviously non-threatening
Rather than having "underlying issues", an alternative explanation: these individuals may be cautious based on a raised awareness, whether due to having friends/family/acquaintances in crime prevention, and/or negative lived experiences amongst their friends/family/acquaintances which bear some resemblance to the park scenario. The NCPC resource linked above states
It’s common for children to think that “bad strangers” look scary, like the villains in cartoons. This is not only not true, but it’s dangerous for children to think this way. Pretty strangers can be just as dangerous as the not-so-pretty ones. When you talk to your children about strangers, explain that no one can tell if strangers are nice or not nice just by looking at them
Rather than taking offense if someone is disinterested in the approach of exchanging contact information to make friends at the park, a family could choose to understand that some people believe in building relationships slowly, getting to know people, and taking time to build trust. As parents are role models, the approach taken by parents when meeting new people may be emulated by their children in future years for dating.
