This is an interesting one for me considering that I celebrate both ancient and modern festivals. This is not because I do not prefer the Reconstructionist methodology for Hellenismos but because the ancients combined religious with civic holidays in their festivals. I try to celebrate many of the ancient festivals as best as I can as a single individual. The reason I cannot celebrate the way the ancients did is primarily because I do not have a Hellenic Polytheist group where I live that I can celebrate with and do not wish to celebrate the “Wheel of the Year” festivals that are common to other pagan paths as they are not Hellenic. This is not that other people celebrating the Wheel is wrong but that those festivals are not correct in Hellenismos because they are religious festivals from other faiths.
However festivals like celebrating Mother’s Day as a festival honoring Apollo, Artemis, and Leto; or celebrating Thanksgiving as a festival honoring Hestia and Demeter are acceptable for me as they are civic festivals that can be adapted for religious use. Because they are civic festivals that have been made into religious ones they are ones that can be adapted by a number of different modern faiths.
But whether they are modern or ancient the festivals need to be celebrated with respect for the Gods in question. Each one needs to be treated individually and researched so that it can be correctly done and the Gods properly honored.