The functions of religion often used by religious humanists include things like fulfilling the social needs of a group of people and satisfying personal quests to discover meaning and purpose in life. Because their humanism constitutes both the social and personal context in which they seek to reach such goals, they quite naturally and reasonably conclude that their humanism is religious in nature hence, religious humanism.
Unfortunately, functional definitions of religion are not much better than essentialist definitions. As is pointed out so often by critics, functional definitions are often so vague that they might apply to absolutely any belief system or shared cultural practices. It simply will not work if religion comes to be applied to just about everything, because then it wont really be useful for describing anything.
So, who is right is the definition of religion broad enough to allow for religious humanism, or is this actually just a contradiction in terms? The problem here lies in the assumption that our definition of religion must be either essentialist or functional. By insisting on one or the other, the positions become unnecessarily polarized. Some religious humanists assume that all humanism is religious (from a functional perspective) while some secular humanists assume that no humanism can be religious in nature (from an essentialist perspective).
I wish I could offer a simple solution, but I cannot religion itself is much too complex of a subject to lend itself to a simple definition that might produce a resolution here. When simplistic definitions are attempted, we only end up in the morass of disagreement and misunderstanding that we witness above.
All I can offer is the observation that, very often, religion is defined in a highly personal and subjective manner. There are objectively discernible qualities which are common to religions and which we can describe, but in the end, which of those qualities take precedence will vary from system to system and from person to person.
Because of that, we must allow that what we describe as the basis and essence of our religion cannot necessarily comprise the basis and essence of anothers religion thus, a Christian cannot define religion for a Buddhist or a Unitarian. For the exact same reason, those of us who have no religion also cannot insist that one thing or another must necessarily comprise the basis and essence of a religion thus, secular humanists cannot define religion for a Christian or a Religious Humanist. At the same time, though, religious humanists also cannot define secular humanism as a religion for others.
If humanism is religious in nature for someone, then that is their religion. We can question whether they are defining things coherently. We can challenge whether their belief system can be adequately described by such terminology. We can critique the specifics of their beliefs and whether they are rational. What we cannot readily do, however, is assert that, whatever they might believe, they cannot really be religious and humanists.

