Government is banned from having a religious requirement for office. But voters reserve the right to consider all aspects of candidates' character. Apparently she hasn't come out on what her religion is. Wikipedia has her as a Roman Catholic with question marks.
If she is an atheist, then voters have the right, even the duty, to consider whether or not that implies a value system difference. If she is not an atheist, then just what God does she worship? And what values does that imply? If she is Roman Catholic then why did she omit God? Is she Roman Catholic for political appearances only? And if so, what does that imply about her character and values?
My statement may not have across well. If she chooses not to say “under God”, then, as you say, that is between her and her constituents, but there is no constitutional requirement that she believe or not believe.