Words and actions are inextricably linked in complicated ways. I don't know anything about who you are or your situation, but I will say that the "sticks and stones" attitude is much easier to believe in if you've never been in a minority group. I used to buy into it, in fact, until a big bag of empathy hit me like a truck as I got older.
Even the conservatives and alt-righters admin this, which is why they're so upset about people using politically correct language, even by their own free choice. "Happy Holidays" anyone?
I, for one, would find it pretty disadvantageous in my studies to attend classes at an institution that endorses (even silently) a viewpoint that questions my right to the pursuit of happiness, to marry who I want, to be the correct gender, or even to exist. Organizations can and do limit that speech in certain environments that they are responsible for.
That said, the first amendment is hugely important, but limited in scope in the consequences that it protects you from.
Of course, it _is_ important to not simply refuse to hear or allow speech that you disagree with. There is a balance to be struck there.