It is important to preserve the rights for intellectual property. From a purely economic standpoint, copyright and other intellectual property laws help artists make money from their work, which is good on an individual and public level.
These are the groups that champion a more restrictive model of intellectual property. These groups consider the mashup to be a derivative work and that without due permission or payment to the original artist it should be against the law:
ACTRA -- Alliance of Canadian Cinema, Television and Radio
MPAA -- Motion Picture Association of America
RIAA -- Recording Industry Association of America