For most Democrats, and for many Republicans, the preferred political stance is one informed by socialism (at least in terms of broadening the "safety net" to cover basic needs - food, shelter and clothing - as well as education, healthcare and employment) in the economic sphere. It is also informed by what may be called progressive secular humanism in the moral and legal sphere.
Most "progressive Democrats" (and many Republicans) today generally pretend to be completely in line with progressive secular humanism. That is to say, (1) they believe their views are founded in science stripped of religion, (2) they acknowledge the existence of a rational system of moral reasoning that can be discovered through rational thought, (3) alternatively, they may prefer to propose that moral systems are inherently mere cultural artifacts with no rational, scientific basis, (4) they subscribe to a governmental system controlled by a class of enlightened intellectuals who understand what is best for humanity and for the world.
Obviously, (2) and (3) are fundamentally at odds with each other, though if you scratch a progressive Democrat these days, you may find that their thinking is insufficiently precise to permit them to acknowledge this point. You will also note, if you dig further, that there is no agreement at a fundamental level on what constitutes a scientifically based moral system, so that even folks who claim to subscribe to (2) tend to operate on a practical level as though they subscribed to (3), with the exception that they may believe their own moral principles (such at they are at that moment) are worth universalizing.
It's important to recognize this in order to appreciate current jurisprudence in the area of First Amendment rights. In particular, it is generally believed (by progressive secular humanists) that it is more important for citizens with unusual sexual proclivities (in the sense of behavior and self image) to be honored and supported (i.e., cooperated with) in these behaviors and self images than for citizens with any religious background to operate in the social or economic sphere in a manner consistent with their religiously formed conscience.
A review of Wikipedia's article on Secular Humanism makes it clear that its dominant philosophical underpinning is what is called Metaphysical Naturalism. Wikipedia's article on the latter makes it clear that it is opposed to any religious anthropology that presupposes the existence of an immortal soul or of a divine being who created us. It is, in other words, philosophically consistent with the view of many naturalists that there is nothing particularly special, in the natural world, about being human.
It strikes me that Wikipedia's article on Progressivism in the U.S. is generally accurate, as far as it goes, but that it tends to be increasingly superficial in its analysis as it gets closer to the present. It also seems to suggest that there is very little historic continuity in the philosophical and cultural underpinnings of the movement over the many decades of its existence. I disagree with that assessment. A lot of the cultural and political artifacts of progressivism from the 1910s, 20s and 30s survive and thrive in the progressivism of the 1970s and beyond, and are particularly relevant to understanding the movement, today.