Wa `alaykum As-Salamu waRahmatullahi wa Barakatuh.
In the Name of Allah, Most Gracious, Most Merciful.
All praise and thanks are due to Allah, and peace and blessings be upon His Messenger.
In this fatwa:
If the nail polish acts like a barrier preventing water contacting the nails, then it ought to be removed before wudu (ablution). However, if the nail polish does not interfere with it, then it is fine.
Answering your question, Sheikh Ahmad Kutty, a Senior Lecturer and an Islamic Scholar at the Islamic Institute of Toronto, Ontario, Canada, states:
If the nail polish acts like a barrier preventing water contacting the nails, then it ought to be removed before ablution. However, if the nail polish does not interfere with it, then it is fine. Here is what I found on the site of those who promote such nail polish; they have this posted on their site:
“Our nail polishes are popular with Muslim women who can now enjoy their manicures and pedicures knowing they are using a wudu (a pre-prayer ablution which requires them to wash their hands and feet) friendly nail polish. Our formula uses a special polymer which enables oxygen and moisture to be transported through the nail polish. Its permeability allows moisture and oxygen to make contact with the fingernails after you have applied nail polish. All our breathable lacquers fulfill tests for water permeability performed in a controlled laboratory environment. The normal nail polishes prevent oxygen and moisture from getting in contact with their nails. For this reason, we consider our nail polishes to be a healthier option for your nails.”
If this can be verified, then it can be worn without any issue. There is no need to remove it prior to performing ghusl or wudu.
Allah Almighty knows best.