I agree with you M0nica when you say this 'make the foreigner pay' little Englander attitude [is] very depressing.
When people say they were charged entry to a museum or gallery in a country other than the UK, are they saying they were charged because they were not from that country whereas nationals of that country have free entry? That seems to be what OP is arguing for.
What counts as “local"? OP refers to council tax when it isn’t council tax which is funding "world class" museums but a mix of central government funding, donations and own enterprise.
Other organisations have different funding models. National Trust has been mentioned. Its funding is a mix of membership fees, legacies, own trading income and enterprise plus grants for specific projects. For example, it receives funding from DEFRA for landscape and species recovery projects. The RHS is largely funded by membership fees and trading income including its national shows.
As I quoted very early in this thread, within the first decade of free entry to museums and galleries, visits to places which which used to charge rose by 151% – the uplift was 180% at the Natural History Museum and V&A, and 269% at National Museums Liverpool.
The latter which received just £20 million in central government funding in 2024/25, includes the Lady Lever Art Gallery, International Slavery Museum, Maritime Museum, Museum of Liverpool, Sudley House, Walker Art Gallery and World Museum.
In total, these attracted over 2.3 million visitors in 2024/25 including more than 600,000 from overseas. Impressive for a city outside of London. Think of how much that is generating for business in terms of travel, accommodation and retail sectors and in turn for the Treasury. It gets a return on its investment many times over.