Instead you'll get atheist or "the wrong religion(tm)" posts being flagged as false. Plus, not all political messages are such that "false will probably do". Which of the following political statements should be marked false?
"The economy was hit hard by the housing crisis"
"Unchecked human industry is negatively impacting the environment"
"Medical expenses are the number 1 cause of bankruptcy in America"
"The US constitution prohibits establishment of religion by congress"
I think all of them are true, but not everyone will agree.
I think as phrased the first statement would not have anyone mark it false. However, people disagree as to the solutions, so once you address those it would be.
The second statement is a widely acknowledged politically decisive issue, so it will be marked false by some.
The third statement is a matter of fact checking, and another response found evidence that it may be false
I don't think people would mark the fourth statement false, but there are always people that want to go into nuances.