First of all, it is permissible to give a non-Muslim some of the Udhiyah meat in charity as long as he is not an hostile non-Muslim or involved in killing the Muslims. If he is, then he should not be given anything.
In this regard, The late Sheikh Ibn `Uthaymeen, a prominent Saudi Muslim scholar said:
“It is permissible to give a non-Muslim some of the Udhiyah meat in charity as long as he is not involved in killing the Muslims. If he is, then he should not be given anything, because Allah says: “Allah does not forbid you to deal justly and kindly with those who fought not against you on account of religion nor drove you out of your homes. Verily, Allah loves those who deal with equity. It is only as regards those who fought against you on account of religion, and have driven you out of your homes, and helped to drive you out, that Allah forbids you to befriend them. And whosoever will befriend them, then such are the Zalimoon (wrongdoers those who disobey Allah)” (Al-Mumtahanah: 8-9).”
Likewise, there is nothing wrong, as far as we know, in gifting non-Muslims with Zamazam water or dates. Rather, Muslims are to be kind and generous with all people, and to set good example for them in morality, kindness, generosity, etc. By doing so, Muslims will make da`wah by means of their practice.