Importance of Not Forcing Polyamory on Others
My take on the resistance to same-sex marriage is that much of it stemmed from the fear that it would be something imposed even on those who wanted nothing to do with it. For instance, a major source of the most passionate opposition in many jurisdictions was from people who feared that Catholic priests might be forced to preside over gay weddings even though their personal conscience and official church policies forbid such actions, or that local Baptist churches would be legally forced to rent their facilities out for gay weddings to be held in them, even when the congregation was against it. However, once they were assured that these things would not happen, a significant portion of the opposition evaporated. This did not make ALL of the opposition vanish, but it did remove a big chunk of it - enough so that in many cases a law legalizing gay marriage passed instead of being voted down.
I suspect a similar force is operating in the opposition to polyamory. There is a portion of the population who interprets toleration of polyamory as meaning that monogamous relationships will now be condemned and treated in a derogatory fashion, and those wishing to practice monogamy will now be interfered with, harassed, and frustrated in some significant ways. To the extent the "promotion" of polyamory is presented as something that will inevitably "replace" monogamy, with monogamy no longer being a viable option for those who want it, polyamory will probably be fiercely and passionately resisted. In contrast, to the extent polyamory is presented as merely one more option to be made available to those who DO want it, but that will not prevent monogamous people from doing what they want, the resistance will probably be substantially less fierce.