Salam Dear Sister,
Thank you for your question and for contacting Ask About Islam.
Covering the truth is the essence of lying. Whether we speak words that are false in order to cover the truth, or we remain silent about an important issue that others have the right to know about, we are engaged in some form of deception. The issue here is whether the current wife has a right to know about her husband’s relationship with another wife or wives.
From a health perspective, there is likely not a significant risk of cross contamination or spreading disease, since there are very strict rules regarding cleanliness and sexual activity. Over and above that, of course, is the direction to only marry believing women from the Muslim community, or from among the Christians and Jews:
“Made lawful to you this day are all kinds of foods, which God has made lawful. The food of the people of the Scripture (Jews and Christians) is lawful to you and yours is lawful to them. (Lawful to you in marriage) are chaste women from the believers and chaste women from those who were given the Scripture (Jews and Christians) before your time when you have given their due bridal dowry, desiring chastity, and not committing illegal sexual intercourse, nor taking them as girlfriends” [Quran 5, Maidah – Table Spread: verse 5]
Having received scripture before the time of Muhammad, peace be upon him, Christians and Jews have similar understandings as Muslims regarding matters of cleanliness, and in treatment of animals before and during slaughter. This makes them close enough in lifestyle to Muslims that they may take believing Christian and/or Jewish women as wives.
I do not know of a situation where keeping things from your wife would ever end well, but every individual’s situation is unique so there needs to be flexibility to allow for solutions to problems to be found.
I hope this helps answer your question.
Salam and please keep in touch.