How old can I let the baby cry it out and how can I be okay with it?

I did not do this with either of my kids until they were sleeping through the night…
Then once I knew they could sleep past a certain point, I was okay letting them cry. For example, when they would slept through the night (12 hours or it could be 10 hours) for 4 or 5 days in a row and then they woke up one night at 5 hours, I would let them cry it out for a period of time—with confidence that they could sleep through the night—and knowing how much better off they were on the days when they had slept longer. If they cried past my designated time period (I always started with something very reasonable like 15 minutes) I would go in, calm them down and then lay them back down and go back to bed. Then if they still cried, I would double the time—next time would be 30 minutes...I was okay with it because I know (based on Babywise) that a rested baby wakes up happy and I don’t want to get in the way of that…
As far as naps, I started from the same period laying them down awake and if it was “naptime” on my schedule, I would let them cry—because again, I knew they full—because we had fed right before wake time and they were dry because I had changed them right before I put them down…Now, again, the occasional dirty diaper does happen right after they fall asleep, and so that is why I had the time period on the cry and when I would go in—I would calm them down and do a little smell check at the same time.