Depending on how this monotheistic religion behaves it actually could be fairly easy for them to obtain full political rights. Assuming that the polytheistic world keeps on the tradition of being open to sub-cults and additions from foreign pantheons then a monotheistic religion that is born from a mix of many different traditions would be just another odd cult that can be allowed to exist, as long as it doesn't challenge the existing political system and legitimacy (which is what caused Christianity to bonk heads with the Romans in antiquity. The Romans couldn't care less if you worshiped Cthulhu as long you didn't cause problem to them, and if you did then they would come for you regardless of the number of gods you believed in, as the Gaulish druids can certify).
So, just have whatever radical political position this monotheistic cult have mellow down, or have the rest of the polytheistic world grow into tolerating the monotheistic weirdos. One has to remember that religious exclusivity and ecumenism (the ideas that belonging to a faith is incompatible with belonging to others at the same time, and that said faith aims at increasing the numbers of its followers through conversions) are fundamental ideas in Christianity and Islam, but not other religions and especially not traditional polytheistic ones. Buddhism is an example of a religion that seeks converts and aims to expand as much as possible but also one that doesn't disallow its followers from continuing to follow their previous religious beliefs, while Judaism is an example of a religion that prohibits its followers from following foreign religious beliefs but (at least in its old school, orthodox form, not the modern one) doesn't seek converts because it perceives itself as the religion of the Jewish people, not that of the Romans or the Egyptians. Most traditional polytheist religions don't care about gaining converts outside of the ethnic group the religion originated and don't care if someone decides to pray to some foreign gods in addition to his own. So, the dominant polytheistic faiths in this timeline wouldn't necessarily have a problem with monotheists existing from a religious point of view, as long as they don't cause actual political trouble.
As for how it would impact the industrial revolution, I think that if you want an example of polytheism in modern industrial societies you can look at modern Japanese Shintoism and modern India (although Hinduism has been heavily impacted by contact with dominant monotheistic religions). It wouldn't change all that much in my opinion, except maybe that non-exclusionary religions may lead to more tolerant societies, but I have no illusion that this will lead to utopian progressive landscapes as proponents of traditionalism and conservatives will simply frame their positions in different ways and have roughly the same strength as OTL.
