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It's similar to people who have the same bad taste in their mouths and say they are, "Spiritual but not religious." Religion is defined as having a set of beliefs or practices concerning theology. So even if your beliefs and practices are your own entirely, you are practicing religion. It doesn't have to be inherently tied to an organized group of people, denomination, or church to be religious.
Our Pagan ancestors were most certainly religious, and they most certainly worshiped, and yet they were not Abrahamic. The ancient Greeks, for example, loved, revered, and feared their Gods, and they didn't believe they were equal to the Gods, but yet they were still the beacon of light for the intellectual, physical, and societal advancement of the Western world. They saw nothing about religion and worship that demanded they be anything less than what a human could, or that they despise said fact. They simply realized that, even with all that humans could achieve, there were still Higher Powers to be respected, admired, and thanked for making life and the Universe possible in the first place.
In the Goodness of the Gods,
Chris Aldridge.