Its something of a fine line. It comes down to this: What you post to a Facebook page, or post on twitter, is the equivalent of walking down your high street,bawling out your opinions through a loudhailer, or parading an image on a sandwich board to all and sundry, endlessly.
So everyone should exercise caution before they post- think before they broadcast their opinion, but ultimately, we should robustly defend the principle of free speech and free expression, and we should not let voices and opinions be neutered just because others might be offended.
And if we are happy to support the publication of, say, cartoons of Mohammed, then we should also be equally happy if others wish to post a burning poppy, or a burning flag.
Only when speech or images posted are clearly outside the law or are a clear example of hate speech or an incitement to violent action should posts be censored, and action taken against the poster, and obviously there will be some discrepancy since a decision on such issues is always going to have an element of subjectivity about it.
For example, it was clearly outside the law to post on twitter the ID of a rape victim, as happened recently. I don't think posting a picture of a burning poppy should be censored.