This is a fake and woke narrative with strong parallels to the hysteria surrounding the narrative of mass graves of indigenous children discovered in Canada. The common element, aside from the falsehood, is the leftist hatred for Christianity, in this case, Roman Catholic nuns, who were providing a charitable haven for unwed mothers (illegitimacy was considered to be a great scandal at the time.)
Debunked here:
https://www.spiked-online.com/2014/06/09/the-tuam-tank-another-myth-about-evil-ireland/
...Most importantly, the constantly repeated line about the bodies of 800 babies having been found was pure mythmaking. The bodies of 800 babies had not been found, in the septic tank or anywhere else. Rather, Corless had speculated in her research that the 796 children who died at the [home for single mothers and their babies] had been buried in unmarked plots (common practice for illegitimate children in Ireland in the early to mid-twentieth century) and that some might have been put in the tank in which two boys in 1975 saw human remains.
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