The problem I have with pharmacists and others being granted such a "conscience exemption" is that they already have what amounts to government-sanctioned gatekeeper status. If you, an ordinary citizen, want birth control pills or any other prescribed medication, you are legally forbidden from getting it on your own; you can ONLY get it through a government gatekeeper.
I do have philosophical objections to any medication other than antibiotics being doled out exclusively through gatekeepers, but forget that objection for the sake of this argument; so long as gatekeepers do exist for such medications, I don't believe they have the right to force patients to jump through additional hoops of the gatekeeper's own choosing, and that's basically what the conscience exemption does.
By contrast, if someone wants to (for example) refuse to sell condoms to unmarried people -- well, that person is a bigoted ass, but in such cases I'd say he has the *right* to be a bigoted ass about such things, because the government does not force you to get a gatekeeper's permission to buy condoms. No condom-seller enjoys what amounts to a government-sanctioned monopoly on his product, the way pharmacists effectively do.