Why would you vote against it? What's the problem with it?
That is, I don't see the difference, in principle, between regulating doctors this way and the WA regulation of pharmacies.
So a state government forces a person to commit murder...and you see no violation of basic constitutional rights?
Several reasons. First, and obviously most important, abortion is generally wrong, not always, but generally. And certainly it is wrong as a mere "lifestyle choice."
Second, government requiring people to do what they don't want to should be rare. Any diminishment of freedom must be very well justified. Taking away the freedom of pharmacists or (more seriously) doctors is not justified just because it lets women (and men) have more carefree sex.
Third, these policies will decrease the quality of health care. Good druggists and doctors will leave their professions rather than go against their beliefs.
So a state government forces a person to commit murder...
Murder is a legal judgment (and unfortunately today abortion is not murder) so let's ask rather whether a person can be required to kill. Consider conscription. Except for religious reasons, conscientious objector status is not required. A person who objects to killing on non-religious grounds can be drafted and sent to war and expected to kill and will be punished if he refuses.
But an important distinction you're omitting is that the druggists (and doctors) aren't required to go against their conscience because they can always choose to change professions. As I've said, this isn't different in principle from requiring landlords, who object on explicitly religious grounds, to rent to homosexuals. The courts have upheld that policy, have they not?