I screen all calls. I know I lose out on some business by doing it, but I feel it weeds out mostly the more impatient or unreasonable types. Our ideal customer has already decided to use our company based on our reviews or a personal referral, and is willing to wait a couple hours for a call back.
This call screening has protected me from dealing with a couple nuts.
I did a power washing job this past summer, that was right on a lake. As I was finishing up, the next door neighbor came over saying that he would need to “see some documentation” of what I was using in my cleaning mix.
I ended up spending a good 5 minutes with the guy trying to allay his concerns. Then, maybe 30 minutes later, the wife comes over and just starts taking pics of the signage on my truck. “Can I help you?” I ask. She gives me the same story as the husband, about the concern for their muddy little stream that was 8’ from their neighbors house, and how it was a protected waterway, on their property.
I take a couple more minutes with her, and email her copies of the SDS’s. At this point, I feel I’ve gone 100x above and beyond what’s legally or ethically required of me.
Maybe 3 hours later, I get a voicemail from the lady, saying she never received the email that “my employee” sent, and to please mail the SDS’s to their PO box 
I did not return the call or mail them anything.
A week or so later, I get another voicemail from this lady, claiming to be interested in a house wash, and what do we use in our cleaning solution. My wife and I were just dying when we listened to it
. She didn’t even bother to call from a different phone number. And she had the most distinctive voice, I don’t know who she thought she was going to fool. 
So I guess my question now is, how do you ‘screen’ people IRL?
One idea I have is to tell somebody that’s heckling me, “Let me text my boss and see if he’s available to talk.” Then get William Page, i.e., the Resident Grump of the PWRA forum, on the phone with them…