I have a half sister from my Dad's second (or maybe third?) marriage, she is well into family history. I did the DNA test to help her try to find my Dad's birth father, he was a war baby, and born in a mother and baby home, and later adopted. Any way, she got quite a long way, and managed to narrow it down to one of two brothers. She also identified a cousin of both of ours, so definitely Dad's side, that was not connected to any other bits of the family she had tracked down.
Long story short, the cousin asked her to please stop digging as his gran was still alive, and it turned out it wasn't just us that didn't know exactly who our grandad was, but the cousin's certainly wasn't the man his gran had married!
It didn't bother my sister or I at all, in fact we were a bit surprised not to have found some more half siblings or cousins. Our Dad had a bit of a reputation himself, and a lot of babies happened in the war from people grabbing at happiness while they still could. But the cousin was quite horrified, so she stopped.