https://en.wikipedia.org/wiki/Christian_perfection
It's the invention of John Wesley. You'll find it in Methodist and, naturally, Wesleyan churches. Whether or not any Baptists follow this doctrine, I do not know. It's a fundamentally flawed position regarding the nature of perfection.
I have a Buddhist coworker who thinks that perfection is possible. We were debating over the matter while he was using a pH meter on some bacterial growth media that he had prepared. If the pH of the media was supposed to be exactly 7.4, then he claimed that he had done a perfect thing, because he had made the media at exactly 7.4. I told him that the meter was only capable of reading to the tenths place, unless he changed the setting. Even then, there was still a limit to the precision of the device. Unless he could find a meter that was capable of infinite precision (perfectly precise) and accuracy (perfectly accurate), then he could not use it to judge his own perfection. It would require an infinite number of digits in the display. Of course, that's impossible. The problem relates to anyone who thinks that any measure of perfection can be achieved in this life. They attempt to measure their accuracy with an imperfectly precise metric. The problem with Wesley and those who follow him is that they seem to think that the nature of sin comes down to such simple things as
thou shalt not commit adultery and
thou shalt not covet, and go no deeper. If you can follow those rules, then you have done well, but Jesus took it to the next step and said that if you even look lustfully at a woman, then you have committed adultery. Even if you follow all of the rules on the larger scale, you can always examine the matter on a finer scale, and you will always see the inherent sin in any person. Anyone who thinks he has no sin is just fooling himself. You can clean a room to "perfection," until you get out the microscope and look more closely, at which point the room magically becomes filthy. The dirt is still everywhere. It's just smaller.
It all goes back to the coastline paradox:
https://en.wikipedia.org/wiki/Coastline_paradox
The Wikipedia article might be a little obscure, but it goes back to the same principle of the metric used to measure a thing. How long is the coastline of England? It all depends on how closely you measure it. Do you measure around every inlet? Every boulder? Every atom? Every electron? The finer the details that you trace around, the longer the coastline becomes. The more closely you look, the longer the coastline becomes. As your measurement approaches an infinitely fine scale, the coastline becomes infinitely long. Similarly, as you stand further back, the entire island approaches a single point. An infinitely large scale of measurement turns the whole island into an infinitesimal point, and the island has no coastline at all.
Such is the nature of the perfection gospel, also known as the Holiness Doctrine. It sees perfection with imperfect eyes. Trust me, if you see perfection in anyone, then it means that you simply are not looking closely enough. There's so much more to sin than simply a list of things to do or not do. It's such a soot that permeates the essence of our being, that there's no escape to be had in this life.