I'm not going to be as thorough with my response, but I'd first like to emphasize on my main pet peeve, is people being oversensitive to PC, I'm the last person to give a damn about PC culture. I say the things I want, and if people don't like it, so be it. That said, I equally don't like the opposite of PC culture, patriotic correctness culture, which is being offended on behalf of a nationality.

it's completely different to equate a dress with a human being.
One's attire shapes culture. Ethnicity also shapes culture to an extent, but you shouldn't dismiss it just because it's an object. From the viewpoint of culture, it has as much value. If it didn't, the outrage over a white person wearing a Chinese dress or a white dude wearing dreadlocks wouldn't exist. The fact that they do does make my point.

Secondly, i am a Greek
I take my point then that Greeks wouldn't be offended. I guess you guys are indeed a little touchy over your myths.

You mentioned that this is mythology and it isn't stated what his color is and how he looked like
That's not what I said. To clarify, I said he isn't white, because he's fictional. When I said white, I meant real white. Real ethnicity can only exist in the real world. Achilles is a fictitious character, therefore he has no real ethnicity.

My issue as i mentioned in my post too, is pushing an agenda that is wrong.
There's literally nothing wrong with the concept of pushing agendas through media. That's one of the main reasons why authors even bother at all. The good stories they write, all push an agenda of sorts. You may not like the agenda that's being pushed, sure, but there's nothing wrong with pushing agendas.

Not only it's disrespectful towards the Author but for the millions of people who grew up learning and loving and even had as a role model each specific character.
I don't know if you realise it, but what you're doing here is political correctness. You're putting fictional characters on a pedestal, and getting outraged over the fact that a character you worship isn't being portrayed in the way you like. The author is long dead. New authors re-invent existing characters all the time.

Just imagine if Black Panther was played by a white blond actor, it would have been completely wrong. Or imagine if we make a movie about ancient China and Kung Gu and it's full of Black,Russians and Greek Kung Fu Masters. This would have been even worse as it's not only disrespectful to everyone, it's also historically inaccurate, like in the Netflix's Troy that was full of inaccuracies.*
All of these ideas actually sound great to me. I'm Chinese by the way, and if they make a movie about Ancient China, and it's full other people from other ethnicities practicing Kung Fu, why would I be mad? Just before you accuse me of not caring for history, oh, I do love history. However, what we're talking about here is a movie, not a history book. If people want to know the real mythology or history, books exist for a reason.

Cultures don't belong to any group. When you're born a Greek or Chinese, you contribute to Greek or Chinese Culture, but you don't own it. This is a simple fact that people don't get. You as an individual, do not get to speak for the entirety of a culture. You only get to speak for part of the culture you experienced, which may have massive variations. And even if you get to speak about it, you don't own it.

Second, what you're doing here again is political correctness. Who cares if some bloke think it's disrespectful? I thought the main idea of political correctness was to be able to say and do things we want, and if people find it disrespectful or offensive, they should just grow a thicker skin and not be such a beta about it.

My point is that you just can't change nationalities and gender of characters already established
Did you know that the story of Aladdin was set in Ancient China, and that Aladdin himself was supposed to be Chinese? But nowadays, people think Aladdin is middle-eastern. And you know what, that's ok. I understand that stories evolve, and people adapt them to their own culture. So my answer to your point is that yes, you can, as proven several times by actual history.