For places like museums and cultural sites, I don't have much of an issue with this. I know that in many of these countries, money from tourists helps keep the museums and cultural sites to be accessible to the people of the country. Even then, the prices are not outrageously expensive. If you feel that everyone should have the same price, that's completely fine. However, I don't know if I would travel to a certain city again, so I will pay the price I am asked to in order to enjoy the museums or other event that I want to see.

In regards to Singapore, I did get to visit many museums, but the only one where I felt was not worth the money was the Peranakan Museum.