Mr. Picard  made the point quite clearly. 
When you are funded by taxpayers you serve taxpayers. 
Full stop. 
Our public services are supposed to be secular and non discriminatory. 
If you work in the public sector your personal morals are secondary.
It must be thus otherwise chaos would ensue. 
"We don't believe in dispensing HIV care"  "We don't operate on women here"
Where would it end?
If it comes to pass that AS is legislated as a legitimate taxpayer-funded medical service then public health services and employees will simply have to adjust.
Those that can't are free to seek employment elsewhere.