Christians of the soul-winning persuasion have encouraged this line of thinking, for the good reason of encouraging each other to evangelism in difficult, dangerous, and discouraging places, but mostly to the detriment of of evangelism in general. At least, in the last century people in the west have claimed it is an obstacle to their embracing belief - it may just be a good rationalisation to hand. Yet rationalisations are at least rational and deserve an answer, even if they are secretly not the real reason.
I recommend to such people some of the writings of CS Lewis, especially in God In The Dock. In brief, his claim is that God revealed some of Himself, even much of Himself, to the other peoples of the world as well, as St Paul also hints. They are not 100% wrong. Indeed, it would be hard to be 100% wrong about anything in eternal truth - even the demons believe in one God, and tremble. (Epistle of James). As a metaphor, God gave all the peoples of the earth pictures. To the Jews he allowed no pictures, but He gave them the captions.
But I have a greater complaint of the skeptics. The adherents of other religions do not object to this claim of exclusivity anywhere near so much. They agree with it, in a sense, except that they believe their beliefs are the exclusively correct ones. Even the supposedly flexible areas, such as China with its Confucian/Daoist/Buddhist mix has the core belief that this very flexibility, whether one calls it fuzziness or accommodation, is itself the key factor. And socially insisting on such is quite an interesting dogma, when one comes to it.
The main group of people who object to this claim of exclusivity, and are quite sure that their more modern understanding is superior, are northwest Europeans or their descendants, living in the last 100 years, who value skepticism and doubt and are proud of taking religious matters on personal experience rather than from authority, and have left the Jewish or Christian faith of their parents.
That seems an even narrower group for a Chosen People, I think.