Except for the most obscure characters in Chinese or Japanes, everything is codified with official lists. Shouldnt we all be following official list unless you choose unofficial character writing.
Mainly, I think, because the official lists differ for Chinese depending on if you use Mainland or Taiwanese lists. So, there’s an inherent disagreement.
Official for each “country”. Does Taiwan completely follow Empirial Chinese?
There are three questions here, I think. One is regarding standards (which I wrote about here a while ago), one is about what individual students should do and one is what Skritter should do.
As @Apomixis points out, there are different standards for how to write Chinese characters (including as kanji in Japanese, of course). This standard also changes over time, so the way some native speakers learnt to write is considered “incorrect” these days. Such differences have little or no effect on handwriting or legibility. This goes for regional differences too.
Then there’s the question of what Skritter should do, which is what I discussed in the blog post linked to above. In short, we try to conform to one standard, but allow other correct or very common variants as well. As you might have noticed, while Skritter only shows you one way of writing, it actually accepts more than one. Try writing 忄for example. You will notice that Skritter accepts writing everything from left to right (the standard stroke order in Taiwan), while showing you dots first, then vertical (Mainland standard). For a vast majority of students, it matters very little which one you use.
As for individual learners, I would go for the official standard whenever possible, but I wouldn’t sweat it. If your teacher, textbook or course shows you one stroke order and that’s what you’ve learnt, then you later realise that it’s technically “wrong”, there’s very little reason to change. This isn’t an excuse to make up your own stroke order, of course, it only applies if you learnt it from some reliable source!