AKMD, your post seems contradictory - you are saying that it is possible for people to grow up thinking that skin colour means nothing more than hair colour or eye colour, but at the same time you are saying that by going to school as a white child with people from different ethnicities you were introduced to different food, festivals and clothing.
I can only presume from your post that you did as a child associate different ethnic groups with these different ways of living, so skin colour then did mean more to you than eye colour, as you say you associated 'asian' people with these festivals and so on.
Unless I am completely misunderstanding and you are saying that as a child you defined someone as being 'asian' due to their clothing and did not realise that 'asian' people (SW Asian? Sorry, not sure what group you are referring to) usually have similar skin tones to each other but not to you.
It seems straightforward to me. Unless a person is a character in a dystopian novel or they work for an electricity supplier call centre, then they tend to treat each person as an individual because it is good manners to do so, as far as possible.
There are many things that define each of us as an individual - I own dogs and don't like getting up early in the morning. But part of the individuality of each person is their ethnicity, religion, cultural heritage, nationality, sexuality, gender and so on. These elements of people's individuality are important to them and should not be ignored.
What does it even mean when someone says they treat everybody the same? The same as what exactly? Usually it means that someone is going to treat someone as being exactly the same as themselves and the people they know very well. That's just lazy, smallminded and bound to end up causing offence at some point.
If we want to live in a tolerant society then we make an effort to show an interest in other people, because it makes them feel as they are valued, and it increases the knowledge and experiences of the person showing an interest, as you found out yourself through your enjoyable childhood experiences.
All of this concern over tiptoeing around, being frightened of saying the wrong thing, worrying about stereotyping people, of having not enough knowledge, of worrying that people from ethnic minorities are over-sensitive, or that the PC brigade are going to get you (as others have said on this thread) is utter nonsense. Being able to bond over what we have in common and learn from things about each other that are different are basic skills for forming friendships and working relationships; you don't have to stereotype or make presumptions about anybody in order to appreciate differences between people. There is no more reason for people to feel they are tiptoeing around someone who celebrates an Iranian festival than there is to tiptoe around me for owning dogs.