Is the widely circulated image that compares bearded men from different religions, and calls for Islam to be distinguished by good treatment, not the beard, a disparagement of bearded men who follow the Sunnah? And is it permissible to publish it to encourage people to treat others well?

There is no need to choose the method mentioned in the question for inviting people to noble morals, as it involves ambiguity and diminishes a noble prophetic tradition, despite its importance in the variation of good deeds. The most distinguishing feature of Islam is the soundness and integrity of its beliefs concerning matters of faith and prophethood, and the greatest thing it offered was leading humanity out of the darkness of polytheism into the light of monotheism and faith.