I think there may be an older answer or two from myself in the FAQ on the topic of South America, but the most recent writeup I did on Reddit can be found here. The short answer is that it is not a fringe theory but that our understanding of the evidence continues to evolve. Some recent genetic studies of people and plants have raised more questions than they have answered-- especially whether sweet potatoes migrated into the Pacific without people about 800,000 BP and whether the crop was therefore domesticated independently in the East and Central Pacific rather than retrieved, acquired, or traded for in Northwest South America. There is no smoking gun one way or the other. Still, based on linguistic evidence and computer modeling, I think most Pacific archeologists accept the possibility, if not the probability, of South American contact at least once.

North America is more complicated. For a long time, there archeologists and antiquarians imagined that Polynesians migrated through North American on their way to the Pacific. There was a strong racial component to this as Polynesians were understood to be akin to, or slightly lower-ranking cousins to, white Europeans (based in part by the pseudo-science of the cephalic index). Even scholars with an indigenous heritage like Te Rangi Hiroa (aka Peter Buck) argued for a North American route to the Pacific (though he later shifted some of this thinking). This route meant it was easier to argue Polynesians were not in fact related to dark-skinned Melanesians or Micronesians. The Nordic adventurer cum archeologist Thor Heyerdahl made a similar argument for a South American start to Polynesian settlement. Both of these scholars were influenced by the direction of winds and currents in the central Pacific which go from East to West. So naturally, they assumed it was just easier for people to travel westward. Hiroa took an even more expansive view and thought that Polynesians had come from Asia and traveled East across the Northern Pacific (again riding the prevailing currents and winds) to reach North America and then set off.

Heyerdhal and Hiroa were not alone in this thinking, but they are two particularly well-known scholars who proved very influential. Hiroa's theories played a role in the Bishop Museum's archeological work in the 1920s and 30s which ultimately began to paint a very different picture and material evidence continually pointed to a West to East settlement.

I would reckon that North American contact remains significantly more debated and more influenced by racialized thinking and religious doctrine. I would not say it's impossible, but the discourse around it is a lot more complicated.

For more on the topic of archeology of the Pacific, as far as I know, the best textbook overview of the subject is Kirch with Irwin offering some still useful computer studies of voyaging and voyaging strategies and Howe giving a wonderful overview of all the different theories (some very crackpot ones) used to explain how people got to the Pacific:

• Kirch, Patrick Vinton. On the Road of the Winds. Berkeley: University of California Press, 2002.
• Irwin, Geoffrey. The Prehistorical Exploration and Colonisation of the Pacific. Cambridge: Cambridge University Press, 1994.
• Howe, K. R. The Quest for Origins: Who First Discovered and Settled the Pacific Islands? Honolulu: University of Hawaiʻi Press, 2003.

For some of the key works of Buck and Heyerdhal see:

• Heyerdahl, Thor. Sea Routes to Polynesia. London: Allen & Unwin, 1968.
• Buck, Peter. Vikings of the Pacific. Chicago: University of Chicago Press, 1959.