I wouldn't abruptly change the subject, because it can be hard to find common interests with people, and, hey, look, we both have kids, let's talk about parenting. It's one of those social grease things. Refusing to talk about it could be seen as being anti-social.
I've employed your DH's method, and while I don't have a lot of friends here, it's not because of blowback from being too honest about my DD. These conversations mainly happen in casual situations where I wasn't going to be bonding long-term with the people anyway... like at the park, or at one of DD's activities. It has often proven to be a topic of mutual interest, and sparked some interesting conversations.
The only time I ever felt self-conscious about it was the one time a bunch of parents were talking about how their kids failed to get into G/T, and all the efforts they were considering (private testing, etc) to get them in. That was pretty awkward, considering that I don't think the floor is all that high, so maybe their kids shouldn't be in it, though I kept that much to myself.
