As has been discussed with previous posts discussing the link between vaccines and abortion, there is significant irony in that both procedures are frequently done as a result of coercion and/or manipulation.
Many women report being pressured into getting abortions they do not want. This is also true for health care providers and vaccines - specifically a yearly flu vaccine.
Receipt of flu vaccine by healthcare providers is increasing. But this is likely only because they are forced to get it in order to keep their jobs. Increasingly healthcare providers are not free to decline a yearly flu vaccine - they do not have a choice.
But here is an interesting irony - pediatricians are free to "fire" a patient from their practice for refusing to comply with vaccination (either in whole or in part), yet healthcare providers who work in obstetrics can be censored, or fired for not complying with a pro-abortion worldview. In other words, pediatricians are free to impose their views of vaccination upon patients - practicing according to their conscience. Yet OB/GYN providers (as well as other types of healthcare providers like pharmacists among others) can be pressured to comply with a pro-abortion agenda - to participate in or to refer - or they could lose their jobs.
Declining to refer for abortion or declining to participate in/perform abortion is not a denial of an essential service as abortion is always an elective procedure. And with >1 million abortions/year (in the United States of America alone) it is hard to argue that women have a hard time accessing baby killing services ... not to mention the damage this does to women themselves. Besides - providers of a variety of services have boundaries or limits of what they will or will not do. For example, many restaurants have signs "No shirt, no shoes, no service" - and as previously noted, pediatricians may refuse service/care for children whose parents decline some or all vaccines.
Pro-life providers do not stop women from getting abortions, nor do they stop those who are pro-abortion from practicing or providing this life-ending procedure. Similarly, those who advocate for freedom in personal medical decision-making regarding vaccination do not stop those who want vaccines from getting them, or from providing them as healthcare providers ... so who is truly pro-choice, pro-freedom? Much like those who advocate for vaccines, those who are pro-abortion may advocate forcing OB/GYN providers into violating their conscience - either through soft or hard measures. Medical students may be carefully screened during OB/GYN residency interviews to ensure those who are placed are willing to learn how to do abortions.
For the moment healthcare providers are free not to offer vaccines - though with the use of electronic medical records (EHR's) as well as ICD-10 and claims data practice patterns (including vaccination rates) will no doubt be monitored and "incentives" to change behavior instituted (ie: payments "adjusted" up or down to "encourage" the desired outcome of compliance with the vaccination paradigm - or else).
We are designed to live in freedom - being given a faux choice is no choice. Being injected with a vaccine in order to continue working is not a choice - it is coercion. So long as there are laws or regulations forcing vaccination for any reason even those who are pro-vaccination cannot claim they are freely choosing to receive a vaccination.