That's a good point NS (about the old homosexuality laws).
I'm as sure as one can be that none of my neighbours claim benefit but I do see people in the course of my work who do. They come to see me and I go to their homes. Many are single parents. I'm aware, without being told, some will do a bit of child minding, cleaning, even hairdressing. It's not my business, "I know nothing", and do not grudge any one of them a few extra quid here and there.
We hear in the media of people who defraud the Benefits Agency by many thousands of pounds but they are rare. The vast majority of claimants don't.
At times someone will find a job, perhaps on a contract, and come off benefit; if and when the job comes to an end, it takes a while for benefits to be reinstated & that causes untold anxiety and hardship.
I always think, "That could be me or mine"; very, very unlikely but none of us know what lies ahead.
As for not having anything to do with someone who has committed a crime, who knows what people have done if you don't know them that well, they don't have to tell you! They're still people. We all make mistakes. I wouldn't hold a past mistake against anyone (I'm talking about petty crime here).
The only thing I would report to the police would be suspected abuse of any kind, if I saw someone legging it across my neighbour's lawn (which I can't really see unless I deliberately look out of one particular upstairs window) carrying a swagbag, dripping silverware and jewellery, or things of that kind.