First of all the question is incorrect, actually its 'Not sinful' and 'Sinful too', and for both(there is no discrimination done here).Before I describe my answer I want to clarify that there's nothing written in any scripts about a women marrying (Vivah will be a more appropriate word) many men is a sinful act.
What marriage is? Its a bonding between two souls, that means the two souls will receive same type of pleasure, sorrow and rewards as they are married. Not only this their Karmas are equally divided. Meaning if wife does something sinful the husband has to be the part of it (either he was part of it physically or not), as they are considered 'Ardhang' of each other and after marriage treated as one.
How its 'Sinful' or 'not Sinful'? If someone has multiple husband/wives, its perfectly sure that their souls would be bonded.
For example, one man marries 2 women.
Case 1 : If one of his wife does a karma, the karma's action will have a result, this result would be divided into 2 parts, 1st to the husband and second to the wife, the left out wife will remain in the Akarmik state. Now if we look through husband's perspective, he is getting dual Karma Results, one from his first wife and other from his next.
Case 2 : If the husband does a karma, the karma's action as a result would be divided into 3 parts, one for himself and other two for two wives each.
Now in either cases we just need to replace the word Karma with Bad Karma or Good Karma, we will get different results, I will discuss one.
If the karma is bad:
Case 1 : The wife will not only suffer from the result but the husband will too, the left out wife will go through the physical aftereffect of the result but not spiritual one.
Case 2 : The husband and his two wives will suffer from results equally.
From above we can clarify that a multi marriage becomes Sinful or not Sinful, depending not only on the depth of multiplicity but also the nature of the nodes(people being married within)
Bottom Note : It's always strictly advised to follow monogamy, as that would lead to equal division in karmas. Not only this the control-ability of that type of marriage is simple, and most off multi marriages suffer from less-controls resulting in wrong Karmas.
There are very less chances of one being so supreme, to take care of others(in case of multiple opposite) all emotion.
It is always suggested to comply with the 'Arthang'(half part) to male/female. The system is always in stable state if equal and opposite charges are kept in the bounds.