In my own life, I have had all sorts of ups and downs, times when it was a struggle to just put food on the table etc. Art and music are my mail pleasures and also lots of different museums. Through university the ability to visit museums and libraries free of charge, not only let me put more into my studies and widen my knowledge, but later as a teacher and lecturer in different places, I was still using those places myself, but used to take students to visit exhibitions , relating to the course. Much more importantly, in my view, I spent a lot of time telling students of all ages about what was available in their area and encouraging them to visit. Someone who is a close friend of mine to this day, I met on a course. She was really struggling as her husband had been killed in an accident and she was the sole person providing for her three children. She did any job that would provide money for her family and fit round the children being in school etc. But she then worked very hard for a degree, using libraries and free entrance to museums and galleries. There was no way she could, or would, take much needed money for her family to spend on herself. She gained a first class honours degree, became a senior lecturer in a university, and set a very good example to not only her own children, but others, teaching them that if it matters enough , there are ways to keep going.
Having one son, I very often took a friend or two with us on days out in the holiday, and because of my own interest in many things but especially music and art, I have introduced many young people to museums and galleries. Knowing so many people struggling to carry on, and in these days of less jobs available etc to have free entry to places is vital. I very much feel that those people who think others should pay, especially while they have the parochial attitude that just because a museum is in their area, that they are entitled. If you look in the majority of museums you will then see many items that are here because the british looted and took things from other countries, so they did not "belong" to britain anyway. The pernicious attitude that we need to divide and split up people instead of encouraging knowledge of the world by all, makes me definitely think of the Margaret Thatcher era , where those who had got more, and those without less or none. Those who want an entrance fee for all are no doubt those who actually can afford to pay it They have never obviously had to think whether you dare go to the museum or keep the money for the school shoes you need to buy for your child!!
As others have said I have been happy to put what I could afford into the box, and have visited the same museum, where on different occasions I have paid nothing, often put £5 in the box, and when I had funds sometimes put £20 in. I am talking about mostly 50 - 60 years ago as I am 81 now. I have never regretted time spent there, have learnt much. introduced children to them , been glad to take a friends little boy with my own. My son of 51 still remembers days out in the holidays where I would make a picnic and then we would go off to a museum or art gallery followed by a visit to a playground where he could let off steam and eat his picnic
So no I do not think we should be charging "foreigners and visitors" They will still be contributing to the economy by paying for accommodation and food. The obvious followers of Farage who thinks that they have the right to insist on such ideas, yet you never hear any of them apologizing for the many things that were basically stolen from other countries. I dont hear them offering to return them, nor admitting how they came to be here. Yet they still think they have the right to tell others who should pay and who should not. In any case even for those who could afford or wish to pay, the cost of having people issuing tickets and taking money would probably mean that the amount ending up in the museums coffers would be very small.