Should we be careful about the coronavirus outbreak for older age groups? at which older age cutoff should people be avoiding public gatherings?

Yes and common sense: Yes, elderly are more prone to develop severe cases and that’s why caution should be exercised when exposure becomes likely. While actual age may matter it would only be 1 factor as chronic diseases and overall functioning level would be more important in this regard.

COVID 19.: Recommend against all public gatherings at this time for any age group. People 65 and older are at increased risk of developing more COVID 19 symptoms.