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.