Islam asks you if you agree that there is only one God, and Mohammed is his prophet. They talk about God and prayer and a few practices, not being Shia or Sunni or Salafi.
When your friends asks you consider meditation and the study and practice of Zen, they don't talk about this or that lineage of teachers.
What is proposed is changing your life, your orientation, your spiritual practice, your beliefs. The invitation to make that change through a particular institution comes later.
We ask people to be grateful, generous, loving, holistic, just, compassionate and self-aware persons. We ask them to start where they are and do their best, and keep trying, to become persons who embody and enact love and peace and justice and reverence in everyday life. We seek, for them and for ourselves, to form a liberal and loving character. That is the goal that we set for ourselves and we propose that they set for themselves. It is what the world needs.
Joining a Unitarian Universalist congregation, or even committing to UUism in the abstract, is only a means to that larger goal. It would bring you into community with others who are trying for that same personal transformation. It gets you in touch with a living tradition of writers and thinkers and activists and leaders who have been seeking the same for decades and centuries. But being a Unitarian Universalist is not the goal of anyone's life.
When people say that they are "spiritual, but not religious", I suspect that what is objectionable to them about religion is its self-serving ways. An institution whose only goal is the success and preservation of itself gets no respect. And that is what organized religion so often looks like. And we focus too much on UU identity, UU growth, UUism itself -- we look like that as well.