Dear Mr. Oren Shkalim
Since there is an overload with questions to the Rishon Letzion Rabbi Amar your question has been passed to Rabbi Aharon Bauron, an important Talmid Chacham
and Halacha expert who reviewed your question thoroughly, following is his answer:
Regarding the question what the Halacha says about closing off websites using "Shomer Shabes",
which, as I understood from the letter, is a program which webmasters can connect to, and it locks their sites on Shabbat and holidays.
What is special about it is that it closes the site according to the sufers' location in the world
For example, after Shabbat here it still doesn't let people from the U.S. in.
I have been asked to pass Maran's answer:
Of course site owners should use this program which saves them from many violations of Shabbat.
It is a great privilage.
Rabbi Aharon Buaron