Religion

Whether or not they have both dogma AND doctrine is debatable, but all have at least one or the other with some providing the ability to opt out of one or the other while still remaining in the club. Regardless without either you don't have religion or anything remotely recognizable as religion.

The only difference is the barriers to some aren't as high as others. It may even be true that the barrier is so low it doesn't present any significant hindrance to the application of progressive policies, but neither does it provide any inherent benefit.

Progressivism as an ideology requires solutions for reform that are bounded by reason. When you incorporate theology that departs from reason, you haven't introduced anything productive and have instead introduced an element that at least has the potential for hindrance whether or not it's realized. In other words, whenever you introduce metaphysical hocus pocus to a reason based approach, you aren't helping regardless of how benevolent those motives might be.