Is it permissible for me to put up a workplace notice that includes a clause penalizing "uttering anything inconsistent with due respect for the religion or belief of others," if the employer obliges me to do so and may be compelled to apply labor law?

The phrase "respecting the beliefs of others" is vague. If it means not declaring the creed of Islam, including its negation of partners and offspring for Allah, or refraining from denouncing those who believe in the Trinity, then this respect is invalid. However, if it means acknowledging the People of the Book in their religion without coercion, insult, or harm, then this is a legitimate form of respect, based on the Almighty's sayings: "There shall be no compulsion in [acceptance of] the religion," and "And do not insult those they invoke other than Allah," and "Allah does not forbid you from those who do not fight you because of religion... to be kind to them and act justly toward them." Accordingly, it is preferable not to display the phrase due to its ambiguity, unless the employer instructs it or there is a law that necessitates it, and there is a considerable fear of harm from refusal.