Electronic flash was no great problem as the duration and intensity was too brief to do much or any damage. It was a disturbance to others and it did allow for taking better photos (if done correctly). Museums banned it so they could more easily sell their own color postcards and prints. They also banned tripods for the same reason. Oh, they claimed they were hazards for other guests, but no more so than the amateur painters they allow in. It was to keep photographers from getting too good an image.
It took a while for them to realize that image-stabilized digital cameras with auto ISO and auto exposure could allow for as good a result as with tripod or or flash. No matter what the "official" reason, It's all about controlling the use of their images for resale.
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