It isn't so much the Easter/Christmas Christians. I mean when you have someone that only has a passing involvement in their religion, it is not at all surprising when they ignore some (or many) of the rules. However you see it in the really orthodox as well. They find what they believe to be loopholes and use them.
Orthodox Jews are some of the best examples:
So Exodus 35:3 says "Do not light a fire in any of your dwellings on the Sabbath day." This relates to Exodus 16:23 which says "This is what the LORD commanded: 'Tomorrow is to be a day of sabbath rest, a holy sabbath to the LORD. So bake what you want to bake and boil what you want to boil. Save whatever is left and keep it until morning.'" Basically the idea is, as far as biblical scholars can tell, that making a fire was a lot of work (try making a fire rubbing sticks together, it sucks) and the Sabbath is a day of rest. So none of that, you make your food on Friday, rest on Saturday. Remember that we are talking the ME/Mediterranean here, so you didn't really need fire for warmth.
However, for whatever reason, the Talmudic interpretation has decided that electricity is fire. I'm not sure why, but that is what the orthodox churches teach. So, you aren't allowed to operate electric devices on Saturday (the Jewish Sabbath), in particular your oven. Well that's pretty damn inconvenient in the modern world... So they find all kinds of "loopholes". You can get ovens that have timers longer than 24 hours. You set them up the day before, and they'll heat up (and down) at the prescribed times. Also while an Orthodox Jew can't go and push the buttons to operate an elevator in their building, it is 100% fine to have a Gentile who does it for you. Or, since elevator operators are a rather unnecessary expense these days, elevators can be (and are) set in to 'Sabbath Mode' where they automatically stop at every floor and open up, and just keep cycling. Takes longer, you have to get on and wait, but you can use it without 'operating' it.
This is real, and it is big. There are plenty of Orthodox Jews that seem to think it is important to obey that part of the bible, but that they can find ticky loopholes and gotchas to get around it and god will be ok with that. I don't claim to understand it, however it is what it is.
On the flip side you'll see some weird stuff like stores that won't let you order on the Sabbath. B&H Photo Video, one of the best camera stores in the US, is like that. They have a big, well designed, online ordering system. However it won't let you order on the Sabbath. You can browse, but if you try to place an order, it won't allow it, you have to wait, it won't queue it into the system. The servers don't get the day off, but they aren't allowed to take orders :).
So you can see how, given things like this, people might assume the Amish would be similar. It is not from dealing with people who are casually religious that you get the idea, but from dealing with those that are deeply religious and seem to care about certain rules, but are 100% fine with going around those rules in tricky ways.
Now lest someone think I'm picking on the Jews here, I just chose the example because it is one you see a fair bit in America. You should see some of the things various orthodox Muslims do that are against the Koran, but they've found a loophole that makes it "ok" in this particular case.