They are VERY relevant today, it's just that they weren't taught to Americans in the history books. Also, not so many people in the American/World public even know of their existence, which is a shame, even for the historical aspect of how much influence they've had in American culture since it's inception.
The third "party" of the United States was the Anti-Masonic Party, believe it or not. Research William Morgan from Bavaria, New York. Read about how incredibly well-coordinated the Masons operated to transfer him out of state, from lodge to lodge, before he was eventually drowned.
Research and read John Quincy Adams, in my opinion, one of the smartest and brightest Presidents to ever live. Funny, I went to Barnes and Noble and checked a biography of him, roughly 400-500 pages long. NO mention of his Anti-Masonry sentiments, which he had and you can read about in his rarely-heard-of "Letters on Freemasonry". Intellectual Freemasons who are interested in the historical aspect of their "fraternity" were nice enough to host a .pdf. You can read his "Letters on Freemasonry" here:
"I shall regret this, because the more attentively I have observed the character of the Masonic institution as it exists in the United States the more thoroughly I am convinced that it is the greatest political evil with which we are now afflicted." -page 78
"It is my deliberate opinion that the Antimasonic party ought not to subside, or to suspend its exertions, till Freemasonry shall have ceased to exist in this country. The career before them is long and dreary, but not discouraging; the object is single, just, and honorable. You have put your hand to the plow. Let it not be withdrawn. For contributing so largely to the end you will deserve to be ranked among the benefactors of mankind." -page 98
"It is, perhaps, too much to ask of you an explicit assent to these positions, because you may consider it an acknowledgment of error. But this is the first and fundamental consideration, from which I draw the conclusion that Masonry ought forever to be abolished. It is wrong, — essentially wrong,— a seed of evil which can never produce any good." -page 111
"The practice of the institution is acceptive and fraudulent. It holds out to him a promise which it never performs. Its promise is light ; its performance is darkness." -page 114