Ten - vasectomies, liver surgery and whatever else Pneumo said.
Ten - you are quite wrong on one crucial aspect. It may be your body, but it is not your right to force someone else to do something that will enable you in your choice.
Hear me out.
Imagine you went to the doctor and said you wanted an operation to remove your nose and ears. It's your body but you cannot expect a doctor to just go along with it.
It is a doctor's job to help you with your health, and it would nice if everyone could agree with everyone else's choices and this particular contraceptive issue never came up. But life is not like that. People have differing opinions. This is not like a vegetarian working in a slaughter house and thus not doing any work; contraceptive and abortion issues make up a small minority of a GPs work and usually there are other GPs that can help you out.
This practice is only acceptable because the GP will send you to another doctor who can help you.
If ALL GPs did this it would be totally unacceptable to deny patient's any access to contraception.
I agree that the GP choice was bad and that this objection should be flagged. And also that practices where ALL the GPs object should be flagged as such so you don't register there if you will need contraception.
But saying that someone should not be a GP because they disagree with this one aspect of care is more than a little intolerant. Can you not find a middle ground?
And just to be clear - I am absolutely pro-choice, pro-contraception, I despise the abortion rules in the Republic of Ireland and all the anti-abortion nuts in the USA. It is absolutely the woman's right to choose and anyone who says otherwise is, imho, extremely unreasonable.