(in response to the OP) and that his statement, in dissent to the denial of cert, has nothing to do with whether he, personally, objects to vaccines (which is what you suggested).
As to the law involved, it is completely irrelevant whether the person complaining about an infringement of their religious beliefs follows those beliefs consistently. (In other words the person bringing the case could have been violating every single religious belief they purport to hold dear and still have a legal right not to be required to violate those beliefs by the state.)
But - under settled law, whatever that means these days, it is an absurd case.
The applicable line of cases starts with Employment Division v. Smith. Smith was a Native American who used peyote as part of his spiritual practices. He was fired for violating state law against the use of peyote and state unemployment services denied his claim for benefits. The court ruled, essentially, that while the state could have chosen to accommodate his religious beliefs it was not required to do so. States are permitted to enforce generally applicable laws EVEN when the particular law incidentally interferes with Smith's right to practice his religion. From the case:
It is a permissible reading of the [free exercise clause]...to say that if prohibiting the exercise of religion is not the object of the [law] but merely the incidental effect of a generally applicable and otherwise valid provision, the First Amendment has not been offended....
Obviously, the object of the state requirement was not to target people who have religious objections to abortion - it was a generally applicable and otherwise valid requirement (mandatory vaccination laws including state requirements for childhood vaccinations as a condition to entering school, have been in existence for as long as I can remember and have survived legal challenges on bases other than violation of religious freedom).
BUT - this is relatively recent in terms of settled law (1990), and I am sure that the fact that the religious beliefs were Native American - not Christian - influenced the decision. (After all, how many parents or churches have been prosecuted, or fired, for giving minors alcohol as part of communion?). With the Christo-centric court we have now - and a violation of certain Christian beliefs alleged - the court could decide that Smith was wrongly decided (just like Roe). Right now it does not seem inclined to do so (6 justices voted to deny cert).
So the case isn't as absurd as you imagine, given recent cases.
And, just so you know, patent attorneys aren't like other attorneys. As a general rule, patent attorneys don't usually like to get their fingers dirty with other law. I'm one of the few whose practice was significantly broader than just patents/IP - and I've also been teaching about 18 subjects (including con law) at a high level for the last several years.
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