Absolutely I took a ton of photos not only for my Google review but pics of the kids as well.
Yes photos are allowed. If there is an exhibit that doesn't allow it will be posted. If you have any questions ask the security staff they could fill you in.
Photos are alowed. No flash only in certain areas due to some artifacts being photo sensitive. The no-flash-photography areas are labled. The signage is not very prominent so be aware. Enjoy your visit, it's a wonderful museum!
Without any concerns I would say.
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