To use one example, I am a volunteer platelet donor with the local blood bank and donate about every other week (providing my iron is not too low). This is something that has no overt religious overtones, but I still consider it to have religious significance because Hellenismos is a religion where we are supposed to help others when we are able to do so. I treat the ACT of donating as an offering of TIME to the Gods and because of that this simple act takes on additional layers of meaning for me.
Another thing that I do is to read, both for my own enjoyment and for Mira’s. The Gods gave us our intellect with the expectation that we USE it. Even if the books I read to Mira are not religious in nature, the act honors the Gods by teaching HER to enjoy books, and possibly later to examine the philosophy that each book contains.
There are other things like my pouring of the first cup of coffee brewed daily as an offering to Hestia, but over time these have morphed into ritual and so do not qualify for inclusion here.