The two arguments that come to mind:

The tests are being used to invoke fear in people and to live your life as a Christian you don't want to support fear. You aren't to fear the deadly pestilence and shouldn't make others fear it either.

You're body is a holy temple and render unto caesar what is caesars and what is god what is gods means that you don't give up your body (i.e. saliva/nasal swab) for ungodly reasons.

And really the law is so unbelievably broad you can argue most anything other than science/politics/medical. If you believe the lizard people on mars had a conference that said god wouldn't want anyone to take covid tests, that could technically qualify - although expect resistance on that.