Frankly, I don’t think how you can nuance “man shall not lie down with another man.”
The author’s argument is that providing a service should be construed as participation or affirmation. Why? Because if Christians truly believe that a vendor service is an affirmation, then they need to explain why it is only gay and lesbian weddings that violate their conscience.
Her argument is that Christians are applying their beliefs INCONSISTENTLY or UNFAIRLY. She then gives examples...
For instance, Before agreeing to provide a good or service for a wedding, Christian vendors must verify that both future spouses have had genuine conversion experiences and are “equally yoked” (2 Corinthians 6:14) or they will be complicit with joining righteousness with unrighteousness. They must confirm that neither spouse has been unbiblically divorced (Matthew 19). If one has been divorced, Christian vendors should ask why.
But Christians don’t do that in the latter case, so, her question is this, why simply target refusal of service to gays and lesbians and ignore other Biblical violations?