@Y.V. Vishweshwar Rao. Good question. I believe marital and family laws shall only remain within the ambit of Civil laws not criminal laws. Only when they get criminalized, they should find place in Penal Code. When an offense under Penal Code is committed, whether anyone gives complaint to police or not, the police has a duty to take cognizance of it, if it is informed. As you said, the wife has no objection, then who else can have objection if a man marries another woman when the first wife is permitting him to do so? Any enemy of that man can have objection and when he knows that police can arrest him and initiate criminal proceedings, he will inform the police and police will file the case against that man under Sec.494 of IPC. That means it becomes an objection to the State, not to the wife of the Accused and State tries to prosecute him and bring him to justice.
What is the interest of State in the personal affairs of those 3 people? When those 3 people have no objection to live together who is the State to intervene and say, bigamy is an offence hence you are liable for punishment? They cannot do it to Muslims because Muslims have their Muslim Personal Law taking precedence over the Indian Penal Code. But people of all other religions must obey the IPC and State can initiate criminal proceedings if any man marries when first wife is still with him as his wife.
In Andhra Pradesh, Sec.494 and 495 are cognizable offences. That means the police can arrest the person indulging in bigamy or concealing the fact of bigamy without a warrant. And we find that Sec.494 of IPC is a compoundable offence as per Sec.320 of CPC. Whereas Sec.495 is not a compoundable offense. There is some sense in it. Though it is an offence, if the spouse has no objection to it, the accused can be acquitted. However, when the spouse is not intimated and the fact of second marriage is concealed with the spouse then it is not compoundable. Which means the law presumes that if it is concealed with the first spouse, then it implies the marriage has no acceptance of the first spouse. And so it is not compoundable offense. However it is also possible that though it is concealed, she/he may accept the second marriage and forgive? So it makes sense to make 495 also as compoundable offence. In fact all family related crimes including Sec.498A shall be made compoundable, bailable, non-cognizable except when it is coupled with the allegations of causing physical injury or death, which anyway can be filed under two sections, like 498A + Sec.323 (causing grievous hurt) or 498A + Sec.300 or 299. Which means, when it is filed under two different sections in which one of the sections is non-compoundable then that offense shall be treated as non-compoundable offense.