As a secular humanist for about 5 years I haven't stepped in a synagogue since then. I've been reading about Unitarianism since then and have been flirting with the idea of conversion.
1. How does one go about converting to UU?
2. Can I maintain my worldview, (i.e. secular humanist, freudian, cultural marxist, ecnomically socialist) in a UU context?
I think 9/10ths already answered pretty well. There is no formal conversion. (Many who join our congregations say that they've been UUs all their lives, they just didn't know it.) Each congregation has different rules about joining but basically you sign a book.
However, just because we don't have a formal ceremony doesn't mean it should be taken lightly (imo). Don't sign the book unless you are ready to make a commitment to the congregation in terms of time and money (in whatever combination works best for you), and heart. Unitarian Universalism is a covenental religion, based on our relationships with each other. When you sign, you are basically promising to be committed to the congregation, and vice versa. You are, however, welcome to participate for as long as you like without making such a commitment. I know people who have been active members of my church for years who have, for one reason or another, never signed the book. That's fine.
As for maintaining your worldview, as 9/10ths said, all views are welcome as long as they do not violate our principles. Our principles are grounded in humanism, so my guess is that you will feel comfortable with them. I would add that tolerance for "theistic" language is also requisite. You certainly do not need to believe in any deity, but do need to be willing to hear others express their beliefs in such terms.
Lastly, speaking from personal experience I would say that while you are not required to change, it may likely happen anyway. After all, what is the point of practicing a religion if it isn't transformative?