Question about wakatte iru

I want to ask about the word "wakatte iru." I learned that it means "I know" and we use it when someone tells us about something we already know very well. Also, it is often used when we are irritated by our interlocutor and want him to be quiet, e.g.
I know! (I'm not stupid)
I know (so you don't need to tell me about it!).
I know (so shut up)

I've read in the internet that "wakatte iru" is a rather rude or snarky word to say. However, is it always seen as rude? I'm curious because I was watching an anime in which two characters were having a chat (instead of going to class) and one of their friends started rushing them by saying "いいから! はやく!" And then one of them replied happily "wakatte iru" . This surprised me because I thought this word is only used when we are irritated and is seen as a bit rude.
I know that anime have slightly different rules, but it still puzzled me.

It's a very slight, subtle nuance, but by nature of being a verb in its present progressive tense, wakattiru carries a bit of a feeling of "I already know that" if it's used as a response/reaction to what someone just said.

Just like in English, whether or not the phrase comes across as feeling rude or indicating that the speaker is irritated depends on the context, tone of voice, etc. If it's said harshly, or as an interruption while the other person is still speaking, then yes, it'll come off as sounding like the person saying "wakatteiru" is upset or impatient. On the other hand, if it's said civilly, and after the other person has stopped speaking, it won't feel particularly rude or aggressive.

That said, wakatteiru will often still have a bit of an "I already know/understand that" nuance to it, and by extension a bit of a "so you don't need to explain that to me/explain it again." Because of that, if you want to make sure your response sounds softer, it's often more natural to say "wakatta" or "wakarimashita." Being in the past tense gives it the nuance of "I understood what you just said," which then carries a bit of a feeling that "I now know that because you told me," removing the "I already know that" feeling.

All that said, the difference is pretty slight, and just one aspect (along with tone of voice, facial expression, etc.) that'll determine whether the speaker is seen as angry or not.

And as for the anime in which one character said "いいから! はやく! and the other replied with "wakatteiru," I'd imagine the person saying wakatteiru was at least partially irritated or flustered, since "いいから! はやく!" is a rude, condescending way of speaking.

Ah, and to add to what I said above, another reason wakatteiru can sometimes sound harsh is that it's the plainer, less polite version of wakatteimasu. So if you're in a situation where you do want to tell someone that you already know something, but don't want them to think you're upset, wakatteimasu might be the better option than wakatteiru.

Thank you a lot! :)

And as for the anime in which one character said "いいから! はやく! and the other replied with "wakatteiru," I'd imagine the person saying wakatteiru was at least partially irritated or flustered, since "いいから! はやく!" is a rude, condescending way of speaking.

After watching the scene again, I noticed that indeed, the character uttered "wakatte iru" in a cool and slow manner (so that the viewer could hear exactly what he was saying), but he had a serene expression on his face. Such a contrast confused me, so I wondered if indeed "wakatte iru" was a harsh sentence or not and what "the author meant." However, you are right, if the character wasn't at least a little annoyed, then he would have used "wakatta" or at least something like "hai hai".