I think the real reason the postmodern church so easily accepts things like inclusivism, i.e., the idea that people can be saved outside of receiving the explicit gospel, is because it is essentially made up of Christless Christianity.
What inclusivism essentially argues is that one can be allied to Christ, not by receiving Him as Lord and King, and thereby cognitively receiving His death and resurrection as punishment of their sins and reward of salvation, but by doing the things that Christ commanded ("love your neighbor" etc.).
The problem is that "neighbor" means fellow covenant member, and we are to love them because they represent Christ and we love Christ. Explicitly.
Another problem is that this is a works-based system, where I become united to Christ, not by faith/confessional allegiance to Him, but by my works. This has the cart before the horse. One is first transformed and united to Christ, THEN he obeys Christ by loving others who are in Christ who represent Him, etc.
Again, it's simply bad theology and ethics that stem from bad exegesis that leads to this sort of Christless Christianity, where I follow Jesus by being loving (according to my own definition of love), rather than I follow Jesus by faith working through love.
Essentially, all of these churches removing Christ as the center of morality and love are setting people up to adopt inclusivism, universalism, etc.