Fortunately, our rescue head is well-versed on health issues and we do not always neuter or spay. Also we are not universally giving vaccines to elderly pets.
My last beloved dog was immune compromised and at the age of four he was not neutered. I was not planning on having him neutered. But then, he got kidney stones and since he was laying out on the surgical table for that Problem, we neutered him while he was there. He was healthier and happier because of it, so that worked out.At the same time we had an unspayed female in our house so that would’ve required separations during her heat cycle, but I was willing to handle that. She died with her reproductive organs intact.