before the excerpt, Roosevelt says, "In Pilgrim's Progress the Man with the Muck-rake is set forth as the example of him whose vision is fixed on carnal instead of on spiritual things. Yet he also typifies the man who in this life consistently refuses to see aught that is lofty, and fixes his eyes with solemn intentness only on that which is vile and debasing." He infers that although the Pilgrim's Progress outlines the Man with the Muck-rake as correct, they are wrong to do so, and that the very message they carry is contradictory. He is NOT telling people to read the Pilgrim's Progress, which automatically eliminates answer 1. Although I could write a long essay about how the goal of this speech is to make regular politicians and journalists seem superior to muckrakers and the character in Pilgrim's Progress, they aren't mentioned in this excerpt, so you can eliminate answer 3 as well.
From there, it needs to be determined if the goal of this excerpt is to draw a connection between the character in Pilgrim's Progress to the muckrakers, or to show the difference. The key to determining this is in the first word of the quote, "yet". Roosevelt first acknowledges the upstanding moral character of the Pilgrim's Progress, and follows this statement by explaining how the muckrakers are not the same.
Therefor, the answer is number 4, "to show the difference between the character in Pilgrim's Progress and the muckraking journalists." My apologies for leaving you this essay to read XD