How does the principle of free speech, as opposed to freedom of religion, apply to this case?

In spite of the fact that this case was triggered by Jehovah's Witnesses students arguing that they should not be forced to salute the flag or recite the Pledge of Allegiance, there is no freedom of religion argument to be made.  At least in theory, a group of atheists could have brought this case. The argument is that the freedom of speech includes the freedom to not speak, to not be compelled to profess a belief, in this case, to not recite the Pledge of Allegiance, and to not salute, since hand gestures are considered a form of speech.  People should not be compelled to pledge allegiance to their country if they choose not to do so.

I would guess there are those who would argue that this case somehow is of use to argue that religious beliefs should be protected to the degree that marriage license clerks should have the right to decline to issue marriage licenses, but the case is of no use as support for such arguments, for any number of reasons, but in particular because it has nothing to do with religion.  Supreme Court Justices usually try to rule on grounds as narrow as possible, so cases cannot be misused later on to make bad law.