What I ask here is for some hint or help on why this specific (and IMO rather minor, as all matters that come too close to relying on the belief of the existence of a deity for their significance tend to be) matter is perceived as so significant by many Christians and Muslims.
Word has it that whole denominations refuse to acknowledge specific others as being "true" Christians / Muslims supposedly because they are Trinitarians or are understood for some other reason to be polytheistic. It is, literally, a deal breaker for many people, and I am told that it requires a considerable effort from some in order to keep their faith that others keep true to apparently important monotheism despite what is perceived as indications to the contrary.
Try as I might, I have so far failed to conceive better explanations for so much worry beyond two very weak reasons.
Seems you are overlooking the Gnostic and/or esoteric rationale for monotheism. I think from this perspective there's a simplistic way to present it, but there's also a (far) deeper way to understand it.
I think the simplistic version would be in vein of one God equals one Reality. Heck, I'm tempted to just leave the simplistic right there, because elaborating on that would be going deeper.
But I desire to go a bit deeper anyway and (at least) hint at the other way of understanding why monotheism is sensible.
I would say Love is the One Reality that binds all (truly) existing things together. Through Love all is shared equally, all are in a continuous existence of gaining / growing. In this Reality, there is nothing that takes away from this, even if there is conviction in notion of lack, scarcity, death, etc. Yet, there are beliefs in this world that amount to lack, scarcity, and death (among other possible such beliefs). This sets up another existence, and may even be perceived as 'reality.'
Where things get deep is a) the realization that this has literally zero impact on (actual) Reality and b) that the believer is (entirely) responsible for this worldview, giving it all the meaning it has for own self. In mere words, that might not sound all that deep, but it gets to notion of really why not place any other gods before (the one true) God. It's not a commandment of that God for that God. That God is going to be just fine. Gaining exponentially, nothing to prevent that. It's a commandment for the believer who thinks (holds conviction) in the notion they are 'not of that God.' Or perhaps more like conveying the idea that all such 'gods' would be beneath who you are (in Reality). So, if instead elevating those gods as above you, then that poses a problem (for the believer). In Reality, they are beneath the believer, but are perhaps currently being treated as above the believer and between the one God and Self. Thus, there's a desire (often) to appease the other gods, and their alleged needs, rather than to work directly with what God is asking of the believer, which is really nothing other than reflection of what the believer says they need/desire most right now, of which God has zero problem providing, as long as what is being asked for, actually exists. Hence how this gets esoteric, fast.
I somewhat feel like going on, but mostly feel like halting here for whatever clarification might be sought, or just to leave it here. The only thing I would add is that the last assertion I made is written in vein, for me, that God (via Holy Spirit, or God's communication link to those who hold any level of conviction in notion of 'I am not God') purifies all such requests, such that there is not something that can be put before God and not re-constituted to serve Creation. How that reconstitution looks, exactly precisely quantifiably is not known to this believer (me), yet I have experienced it. More than once, and feel confident everyone has. As an example of what I speak, I may ask God for more money, because I see that as something that is between God and me, as in it has power above my own self and thus is 'higher' than me, but beneath God. While God (I imagine) treats it for the nothingness it actually is, and hear's request of "I'm feeling lack of abundance, please remind me of how abundant I am as God." And how that plays out circumstantially may vary, but the principle (of abundance) would be fairly consistent. The circumstances may be 'vastly different' but all that could be simply filtered through the illusion that it is (thus really no different, but may be treated as otherwise, based strictly on appearances). And I'd just add in kicker that the prayer request could (likely is) answered in a way that is rather immediate, but given that I'm asking for "more money" I may not recognize it being answered immediately, or even possibly see it as not answered at all. I may actually get very clear indication of how abundant I am right now, but overlook that in favor of the god (money) that I've placed between God and me.
And I was responding to BOTH you and 
