They are claiming that the museum is being built on ancient graves, while the Simon Wiesenthal Center says that they are only building on top of the site of an existing parking lot and not touching the remaining part of the cemetery.
So, let's see how much respect Muslims themselves had for their own sacred cemetery 65 years ago. From the Palestine Post, November 22, 1945:
An area of over 450 dunams in the heart of Jerusalem, now forming the Mamilla Cemetery, is to be converted into a business centre. The townplan is being completed under the supervision of the Supreme Moslem Council in conjunction with the Government Town Planning Adviser. A six-storeyed building to house the Supreme Moslem Council and other offices, a four-storeyed hotel, a bank and other buildings suitable for it, a college, a club and a factory are to be the main structures. There will also be a park to be called the Salah ed Din Park, after the Moslem warrior of Crusader times.So, when Muslims build on top of a Muslim cemetery it is fine, but when Jews do the exact same thing (even when they are not!) it is a major crime.
...In an interview with "Al-Wihda." the Jerusalem weekly, a member of the Supreme Moslem Council stated that the use of Moslem cemeteries in the public interest had many precedents both in Palestine and elsewhere....
(If you want to see how the Times-UK bought the Palestinian Arab narrative hook line and sinker, see here. The Wiesenthal Center response is here.)