The post states that Cruz's mother took up with an Englishman, moved to England and married him while still married to her previous husband. The marriage to the Brit would have granted her British citizenship.
She had a boy child who subsequently died, after which she returned to the US. Shortly after, she met Raphael Cruz (who was also still married to someone else) and they moved to Canada.
According to Canadian immigration law, as a British subject, she could become a Canadian within one year.
So, it doesn't appear that the word "loyalty" was in her vocabulary, as she applied it neither to her men nor her country.
What a mess. There are suppositions here but...what was her nationality when Ted was born in Canada?
The offer of British Citizenship does not automatically strip away her US Citizenship.
My understanding is that it can only be relinquished by a deliberate act of renouncement. Absent that, it doesn't matter what the laws of other nations say about it. In the US, US law applies.
Also the bigamy references are just pot-shots at her character, and have nothing at all to do with the legal issue of her citizenship status.
Yes, bad people still retain the rights of US Citizenship.