Japanese pitch accent actually varies across regions. Some have no pitch accent at all! I think this shows that it's not very important unless you want to sound like a native speaker. I never bothered to learn the "standard" pitch accents but I tend to imitate the Kansai pitch accent of my wife :)

In Japan/ese, the pitch/stress thing is overrated, and so are regional language differences. When natives point it out to me, it strikes me a little more than cultural gatekeeping. Linguistic context matters much more. How often are you listening to your own native language and you are confused by two words that sounds similar (like 'hashi' in Japanese for bridge/chopsticks)? Almost never. Advice: Ignore it when natives that criticise your pronunciation. Ask them how is their German or Thai is... and they will freeze with shame.

Where I come from, to criticise a non-native speakers accent or small grammatical errors (that do not impact the meaning) is a not-so-subtle form of discrimination. As a result, I never do it. (To criticise myself, it tooks many, many years to see this about my home culture and stop doing it myself.) Still, many people ask me: "Hey, can you correct my <language X> when I speak it?" "Sure!" (but I never do.)