No, you really need the 'that of'--otherwise, you turn the Metropolitan Museum into a library, and it is not. 'That' is a pronomial referring back to 'art-related reference and research library' (which is conceived of as one entity-- I would perhaps have chosen 'those' instead of 'that', because it seems to me that 'reference library' and 'research library' may be two different institutions). The equivalent to 'that of the Metropolitan Museum of Art' is 'the Metropolitan Museum of a Art's art-related reference and research library.
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