Antivaxers frequently object to the use of fetal cell lines to manufacture vaccines on "moral" grounds. Über-quack Joe Mercola lays down some astonishingly bad moral arguments based on pseudoscience.
The Italian antivaccine group Corvelva published a really bad "scientific report" claiming fetal DNA in vaccines is dangerous based on a dubious next generation sequencing analysis whose methods are not described. It's not. To believe its claims, you have to believe that DNA can do anything.
Antivaxers frequently try to appeal to antiabortion activists by claiming "fetal parts" are used in vaccines. In Michigan, they're trying to enshrine such deceptive efforts into law in Michigan Senate Bill 1055, which would mandate "informed consent" regarding vaccines for which fetal cell lines are used to grow the virus. In reality, this would be misinformed consent and a strategy to frighten parents out of vaccinating.