Why is it more acceptable to get rich doing sports than business? I live in Finland where it is not acceptable to emphasize of being rich, eg. buying expensive sportcars/houses/apartments and introduce them on "yellow press".

But there is one exception. If you have earned your money doing sports (eg. playing ice hockey, driving Formula One) it seems to be totally acceptable.

What is the psychology behind this?
It's all about what people think are your motives for what you do, how hard people think you work for your money, and how nice people think you are.

If people think you earn money just because you love money, you can easily come off as cold and less pro-social. That makes people skeptical of you.

A bias makes people tend to think that whatever work they don't see you do, you never did (personal experience). This makes people value you less and admire you less if they can't actually see your contributions to society. Most office-work is prone to this bias.

People tend to see social people as more nice than less social people, and like them more. This is likely due to the advantage our race gains from social cooperation, which we would not have survived without. We prefer people who we think we can cooperate with and get well along with. 

Talking about getting well along, we also prefer people with whom we share any interest, hobby, attitude, history etc because it increases the chance we get well along with them. Birds of a feather flock together.
This means that 1) We prefer people we know are social and 2) we prefer people who share some of our interests.

Business people will go well along with their kind. They might not be very fond of athletes.
Athletes go well along with their kind. They might not be very fond of business people.

Fact is, that which of these "professions" is more popular depends entirely on who you ask and the circumstances.
So I take it you wonder why the general attitude is that business people are less popular than athletes. Well, that's because most people feel they have more in common with athletes (who share their passion for sports) than business people.