I do think that no matter what you believe you should be prepared that there will probably be MANY people who disagree with you. And it's not a reason to be hateful, from either side. It seems the conservatives are always hateful to the liberals (while trying to bully them into believing something), and the liberals are fine hating them right back and treating them in the same manner (while calling for tolerance and acceptance). I am definitely conservative in my views but hating other people for not believing the same kind of defeats the purpose and pushes them away.
That being said, if you truly believe something, you should know how to defend it, be able to explain it to others, and be willing to stand up for it. You definitely have to choose your battles as well.
On the religious front, I'll say that if you believe that your beliefs are Truth (not truth to you, but Truth), then I do think you have a duty to share that with those around you and with the world. A true Christian that believes that Jesus Christ is the only way to God (according to the Scripture), and everyone who does not follow Him is on a path to eternal damnation, then they should share the saving knowledge of Jesus Christ. Does this mean they should be judgemental, degrading, condescending, or try to bully someone into believing? No way! My job as a Christian is to try to glorify and exemplify God so everyone who meets me will be drawn to Him (and I fail miserably at it most of the time). But He is doing the drawing and the saving, I am just a tool.
There has to be absolute truths in some instances, like religion and morals. For example, with morals, if someone says that stealing isn't wrong because it isn't wrong to them, if there is no absolute truth that says it is, then why can't they steal? In cases where absolute truth exists I would say that those who believe those truths should stand up for them (in a respectful manner). As another poster said, it's a delicate, rarely achieved balance.
But in other cases, like your vaccination example, it doesn't really have an absolute (as far as I know, I've only researched it a bit and plan to more if I ever get pregnant!), and are probably the battles less worth fighting. Just ignore her and go on