Has anyone in America not been allowed to marry because they failed the blood test, although they have a child?

You can;t "fail" the blood test.

The blood test, when it is used, is to inform you and your fiance AND THE GOVERNMENT of any hidden sexually transmitted diseases you might have, and to test your bloods RH factor, which, in some cases, can kill a fetus if your doctor doesn't know about it and take immediate action.

NO ONE "fails" the blood test.

There HAVE been cases where close cousins have married, had children, and then the children are taken away and placed in foster homes.

The blood tests used to be done in most states for making sure there were no STD's. Usually the test was for syphilis which can have fatal effects on the brain. I can't remember which famous gangster died from syphilis Syphilis is easily treated now with antibiotics.. Now days I don't know of any state that still requires blood tests. Nothing against you but maybe they should require a blood test for plain old stupidity although that can't be treated!

Not every state has blood tests. And it's not a pass/fail thing.

You don't need to pass a blood test to get married. You just need to have one, so you'll know about potential problems.