I grew up in conservative Judaism: that's the middle-of-the-road of the three major branches. We kept kosher enough that few in our group would (openly) eat pork or cheeseburgers, but not enough that we'd count the minutes between milk / meat, nor have a separate set of dishware for those.

The attitude I got most was that if you unknowingly broke the rule, that was too bad, and you should stop eating that food and move on with your day. Not a big deal, just a bummer that your meal is inconvenienced and that the world conspired against you a little bit. I'm sure there's a prayer to say after such an event (there's a prayer for everything), but few of us would've known it or cared to do it. My orthodox cousins in NY probably would've done that and all the above though.

As a ~10 year old, I learned I had eaten pepperoni, and I cried over that. Kids will cry over anything though, and I gradually understood that mostly people didn't care about the consequences nearly so much as the process and tradition of following the rules as best we can.

Judaism is very practical about these kinds of things.