你的这句话应该是错的,正确的应该是：They feel that it is important to remain popular with their friends.这个句是个宾语从句,that it is important to remain popular with their friends 是feel 的宾语；而 it 是一个形式主语,代指 to remain popular with their friends.
译：他们感到受朋友们欢迎（喜欢）是很重要的.