Yet, on the same movie, we see him do other things than protocol. Why is this so wrong with TPM but not wrong with ANH?

Because while there's nothing wrong with a protocol droid doing something non-protocol related, that's quite a different issue than specifically building a protocol droid to help a homeless mom do chores around the house. That's like me writing a Greek lexicon for my wife, who has absolutely no use for the ability to look up the English definition to Greek words. Sure, she could use it as a paperweight...but if that's what she needs, then why not just give her a paperweight to begin with?

Her son thought she did need help at home, and happen to find pieces of protocol droid, which from a physical point of view looks way more helpful than an astromech for chores.

Ok, but RLM isn't debating whether or not Anakin, on finding some pieces to a protocol droid, should or shouldn't have gone ahead and put them together. He's debating the storytelling merit (or lack thereof) of using this as a subplot. The issue isn't so much whether or not Anakin, if given the opportunity, should've build a protocol droid; it's whether or not George Lucas should have written that into the movie.

And however you rationalize it, Anakin building C3p0 is just mind-numbingly stupid. For one thing it's fanwankery, pure and simple. For another, it shrinks the universe and introduces a level of "convenience" that stretches credulity beyond the breaking point. Then of course, to top it off, there's the fact that a junk dealer's slave would have no need for a droid specifically designed for etiquette/protocol and translating over six million languages.