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 Gcd Himself who declared so - nobody made up the rules, we got them from Gcd.
Note that the first 2 of the 10 commandments are:
By worshiping anything else you are trying to degrade the Uniqueness and Power of Gcd, by equating him - at some level - to the other item(s) you worship. This is affront to Gcd 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)
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:
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 (the Jewish concept of G-d) is limited and shares power/dominion over Creation with other entities.
If this were true, H"V, it would result in neither deity having absolute power/dominion and, therefore, 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.