The phrase "Bless your/his/her heart" is quite old, and yes, it has a religious connotation. When someone does something in an obvious attempt to hurt or offend someone else, they are considered to have an evil heart. We all have evil hearts according to the Bible, but follow me, please. We ask God to bless their hearts in the hope that they will turn from their evil ways. When you say "Bless your/his/her heart", you are in effect saying in a nice way that that person is evil, and intentionally hurt the victim. This is why the phrase is considered offensive to the subject.
This has a similar origin to the phrase "(God) bless you" when someone sneezes or coughs. Back in the old days, sickness was considered a direct result of sin. It is actually an indirect result according to the Bible, but over the years this was misinterpreted, mostly with the help of John Calvin and his followers. Saying "(God) bless you" to someone is saying we hope God cures them, not only of the sickness, but of the sin they committed to deserve the sickness in the first place.
Please, no comments about how Christianity and/or Judaism are/is a myth. It is a tired argument, and is no more proveable than its being factual. - LJS
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Long John Silver
San Diego, CA, USA