The question whether "there are infinities" or whether mathematicians believe in them is nonsensical. One can define extensions of the set of real numbers which contain infinity. These extensions then lose some of the field properties of the real numbers. Cardinal numbers which measure the size of sets are not only infinite, there are an infinite number of different ones.
The fool hath said in his heart, There is a God. They are corrupt, they have done abominable works, there is none that doeth good.
Psalm 14, KJV revised edition