Postmodernism is a danger to the pursuit of truth in general. It's also an impediment to any kind of societal cohesion. In its current form, it exacerbates societal division.

Yes, I'm concerned about postmodernism as a Christian. But I'm also concerned about it as a member of the human race. Even if I weren't a Christian, I'd still be condemning postmodernism and warning people against it.

But...to answer your question... postmodernism's specific danger to Christianity is that it denies any truth claims. The Bible says "God is truth." The postmodernist believes truth is relative and that the very pursuit of truth or claims to the truth represent power dynamics between identity groups. Postmodernists (especially today) see Christianity almost exclusively through the lens of social power dynamics.

To the postmodern thinker, the claim "Jesus rose from the dead" isn't evaluated against any evidence. Rather, it's evaluated according to how this claim makes some people FEEL and how that claim might be used (or has been used) to create power structures or imbalances which have negatively impacted some people or identity groups.

While I believe, in the spirit of "Love your Neighbor," we should be aware of, sensitive to how people have been negatively impacted by powerful people, organizations, or movements... and we certainly should oppose injustice... we also have a responsibility to pursue the truth. Refusing to do that helps no one.