So, how do I get out of this contradiction? The answer is obvious: what is the public harm from the individual beliefs? For vaccines, we have so much science (and thanks to the recent anti-vax movement) and recent outbreaks that demonstrate that individuals refusing to vaccinate their family do pose significant public harm. Easily preventable diseases become a threat again.
For niqabs, what is the public harm from individuals wearing a garment that poses no threat?* Not much. There will be those who say it sends signals of oppression, because in some societies women are required to wear such things. In Canada, people are not. If a woman does not want to wear it and is being oppressed by her family or spouse, then there are the usual means to deal with such stuff--the laws dealing with abuse, shelters, hotlines, websites, etc. But this again is not the niqab posing harm to the society. Again, Canadian society is strong enough that its values will not change due to a few niqab wearers.
So, I can be consistent in my core values (and core Canadian/American values) that state power can/should be used to overcome individual religious freedom when there is real harm threatened to society. Not vaccinated = harm. Wearing niqab = no harm. It is that simple. Liberty should only be sacrificed when it threatens the safety or rights of others. A friend insisted that there is a liberal argument to be made on both sides of this debate, and the answer is: no, there is not.
* This is where it is ironic that some Sikhs have been loudly against the niqab given that some Sikhs carry knives as part of their religious observance. And knives do pose a bit more of a threat (not much, but more) than a niqab--pretty sure there are more knife wounds than, what, chokings by clothing?