Nonsense.
No-one I have heard has suggested that faith-based organizations be "forced out of business".
The point is that they are tax-supported, supported by public funds. They are therefore required to obey the law of the land.
Which, in this case, is structured to satisfy, at least to some extent, patients.
Patients.
Not providers. Or boards of directors. Or anyone else's conscience than the patient's.
If the people who run these faith-based organizations refuse to adhere to these rules, they are entirely entitled to fund themselves, as charities, or whatever.
But they are not entitled to one red cent of my tax dollars. Or anyone else's.