A person was given the Kibud of Sandik at a Bris Mila, conducted by a Mohel Talmid Chochom and Yereh Shomayim merabim; Some members of the family requested no Metzitza bePhe, and the Mohel in such a case does metziza with a Keli. Now the Sandak wants to reject his kibud as a Mochoah. Is he allowed to reject?
There is no prohibition against rejecting a kibbud, and he is permitted to do so.
However, he should think carefully if this is the correct way to act.
There are many authorities who permit the performance of metzitzah with a keli, and this is the common custom among certain communities.
It is true that among the Haredi communities it is still customary to perform metzitzah by oral suction, and that some Hungarian poskim cling to this custom with great zeal, but in a halachic sense performing suction with a vessel is fine, and therefore the act of rejecting the kibbud, which might be very offensive for those performing the Bris, should be weighed up carefully.
Please see here for a short summary of the issue.