New York prohibits service of civil process on the first day of the week unless in a criminal proceedings or where authorized by statute. Service on a person known as a religious Saturday Sabbath observer, if malicious, is a misdemeanor.
The answer provided to you is in the nature of general information. The general proposition being that you should try to avoid a bad outcome if you can.
I am an attorney and the owner of a process service company. We never serve papers on legal holidays when the the Courts are closed because the licensing agency frowns upon it although Courts do not generally mind.