Jim, I've seen similar postings from others who feel as though they have been taken advantage of by Ancestry.
I think most of the free trials are for only 14 days, so if you don't cancel before that period ends then it's considered that you want to continue the service. The notification is the responsibility of the user, as far as I know, since I've never tried the trials.
I've been an Ancestry subscriber for many years and I always get a personal phone call about a month before my annual subscription is due to expire. The phone call is not only a notification, but a tool to try and sell even more services on renewal. I have upgraded via the phone calls a couple of times, and was given a free month or two for doing so.
I don't consider Ancestry to be trying to rip off people. They have always done what was promised to me in accordance with the contract terms. That's just my opinion based on my experiences in dealing with Ancestry.
If you don't want automatic renewals, just cancel your credit card and get a new number.