Society has absolutely no right to dictate the forms that personal relationships between consenting adults can take.
"Marriage" is an artificial construct. Monogomous or polygamous, there is no need for "legal marriage" in a free society, nor would a communist society hold such unions above any others.
Insofar as to why marriage is so promoted as "ideal", it all goes back to property and money. Monogamous marriages simplify inheritance and lineage, they keep right of property lines clear, and straight and helped to keep feudalism, and to a lesser extent capitalism, running less messily.
The "nuclear family" structure is an inherently conservative institution and more and more evidence is demonstrating that it is in no way nescessarily a desirable one.
A post-revolutionary society would radically change the way that the family operates.
As far as religion is concerned, you are correct in that the Bible and Koran look favourably at polygamy. They are, however, deeply opposed to polyandry. Again, this is to preserve inheritance and, also, to keep women subjugated.
However as communists, we obviously don't give a damn what "God" has to say on the subject. We can be quite certain that whatever the topic, "His" opinion is utter garbage
I'd love to change the world, but I don't know what to do, so I leave it up to you...