To be throughout:
(...) the chirality of all molecules would have been inverted.
It would not, and here is why.
Two examples of these ubiquitous, essential molecules are carbohydrates and amino acids. In all organisms on Earth, most carbohydrates are found in what is known as the D configuration. The "D" stands for "dextrorotatory" but the nomenclature is confusing. For carbohydrates, the configuration is defined as relative to glyceraldehyde, a simple sugar. Thus D-fructose or D-glucose have the same configuration as D-glyceraldehyde, but only D-glyceraldehyde is guaranteed to be dextrorotatory.
Amino acids in life on Earth are predominatly "L", meaning they share an absolute configuration with L-glyceraldehyde.
So humans, like most life on Earth, is made of a mixture of levorotatory and dextrorotatory molecules. Some types of the molecules in humans are predominantly dextrorotatory and some are levorotatory.
Supposing chirality did behave as assumed in the question, it still wouldn't be so simple. The complex molecules that form living being aren't symmetric in only one plane. On top of that, the enantiomerism we learn in high school usually deals with only small molecules that usually have only one stereocenter. A protein may have thousands of stereocenters, and flipping all of them may not be feasible.
For example, this is the human hemoglobin:
It's called "globin" because, looking from afar, the whole molecule may look like a globe. Looking closely you see that it is made of many carbon chains. If you just twist each stereocenter the other way around, they will tend to twist mostly outwards. If a protein still forms, it will tend to be concave instead of convex. It will probably not work as an oxygen transport protein anymore, or less probably it will still work but less efficiently.