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She isn't the kind of insensitive girl who would laugh at a funeral.
Literal
She [topic-は] funeral [at-で] laugh [extent-ほど] insensitive girl is-not.
~ほど ('to the extent of') here marks the degree of insensitivity needed to laugh at a funeral — '[insensitive] to the extent of laughing at a funeral.' The whole clause 葬式で笑うほど無神経な ('insensitive to the extent of laughing at a funeral') is a relative-clause modifier of 女の子. Funerals (葬式) in Japan have strict etiquette — black attire, restrained behavior, prescribed greetings — making them a particularly weighty setting for an etiquette violation.