You are not allowed to ask for personal requests on shabbat and yom tov when praying to god. However the elokay nitzor following the amidah has a format of a request and is yet still said on these days.
Why is this the case and is it any different the the remaining request-like blessings that are said in the amidah during the week (e.g. refaeni, selach, barech aleynu, etc.)?
The same could be asked regarding the yehi ratzons of the birkhot hashakhar.