What is the wisdom behind declaring Idolatry as a cardinal sin in Judaism? What is wrong if the true God as well as some other person\Object is worshipped along with him as long as he is not leaving the worship of the God of Israel?
You make it sound like somebody declared idolatry to be a cardinal sin.
But it was G-d Himself who declared so - nobody made up the rules, we got them from G-d.
Note that the first 2 of the 10 commandments are:
- To believe that only He runs the world (so it makes no sense to worship anything else)
- One may not worship anything else besides for G-d Himself.
By worshiping anything else you are trying to degrade the Uniqueness and Power of G-d, by equating him - at some level - to the other item(s) you worship. This is affront to G-d which He declares (in the 10 commandments) that he will punish severely.
The reason God considers it a capital offense is because it is incompatible with Judaism. i.e. Once you start worshipping other than God, the foundations of torah observance falls apart. You now have several masters. You cannot fully place your trust and hopes in God and therefore cannot worship Him properly
Here's a quote from the shaar yichud of chovos halevavos (start of intro)
After investigating after what is the most necessary of the cornerstones and fundamentals of our religion, we found that the wholehearted acceptance of the unity of G-d is the root and foundation of Judaism. It is the first of the gates of the torah, and it differentiates between the believer and the heretic. It is the head and front of religious truth, and one who strays from it - will not be able to perform religious deeds and his faith will not endure.
Even so, some sins are actually worse than idolatry but are nevertheless not capital offenses. Being hypocritical in one's service is in some sense worse, but at least it is not totally incompatible with Judaism. You have to start somewhere. Here's a quote on this from Chovos Halevavos gate 5:
Similarly we can say for the idol worshipper, that ignorance of G-d is what brings him to this (he hopes to get benefit or protection from the idol). However, the idol worshipper is to be preferred over the flatterer (hypocrite) in the following four ways:
(1) In our times, there are no prophets which can perform miracles to clarify to the idol worshipper his faulty outlook, but the flatterer in G-d's torah (who performs the service of G-d to impress people, as above), there are grounds for a claim against him, since he undertook the commandments to serve G-d alone and undertook the prohibitions not to serve someone else (than G-d).
(2) The idolater worships something which does not rebel against G-d (sun, moon, stars), but the flatterer in G-d's torah worships a human being who rebels against G-d as well as one who does not rebel against Him.
(3) The idolater worships one thing alone, whereas for the flatterer, there is no limit to those he worships.
(4) The idolater's status is visible for all to see, and people guard themselves from him due to public knowledge of his denial of G-d's existence. But the flatterer's denial is not visible, and people trust in him, therefore he is more likely to damage them (influence them with his false beliefs) than the idol worshipper.
One can apply the same idea to explain the capital punishment incurred for adultery or incest. These things are incompatible with a torah society and if left to go rampant will irreparably ruin it.
To make the question stronger, the Rambam writes (Hilchos Akum 2:1) that the primary belief of idolaters was/is that G-d is in charge and the idolatry gets its power from Him. So, if we still believe that G-d is the Boss, what's the problem?
I once heard an explanation that the problem is that if you have an intermediary, all you will care about is what the intermediary wants. If there is someone "directly" in charge of you, you won't care about what the "superior officer" orders, as long as the entity you are dealing with is happy. So you essentially sever your relationship with G-d by relating to some other entity as having jurisdiction over you.
I do not yet have sources for this; but, having considered some implications of idolatrous belief, I will pose an answer.
Idolatry ("`Avodah Zarah" in Hebrew) stems from the belief that Hashem (i.e. G-d) is limited and shares power/dominion over Creation with other entities.
If this were true, Heaven forbid, it would mean that no deity has absolute power/dominion and, therefore, each deity having relative power/dominion. For example, deity1 may have dominion over the Sun and deity2 over the Moon.
What happens when the two or more deities express conflicting demands? What happens when believerA abides by deity1's command which necessarily contradicts believerB's abiding by deity2's command?
This may be a tad reductio ad absurdum; but, this multi-deity system effectively results in moral relativism. I do what I want, because it aligns with my beliefs. And you do what you want, because it aligns with your beliefs.
This is, by definition, the polar opposite of moral absolutism: in our parlance, a single-deity, absolute system of beliefs. In short, the belief in one G-d with absolute power unites Creation, whereas the belief in multiple deities with relative power divides Creation.
EDIT: BS"D, after five months, I've stumbled across a Chabad.org article written by Rabbi Tzvi Freeman stating effectively the same conclusion as regards idolatry's or polytheism's catastrophic effect on the world.
EDIT: BS"D A few years later, I listened to a shi`ur by Rav Shemu'el Eliyahu in which he strengthens my points albeit more succinctly: ahdut (unity) symbolizes `Avodat Hashem whereas perud (disunity) symbolizes `Avodah Zarah.