That sort of thing which you wrote, is so messed up it is difficult to know where to begin.
Semi-pelagian? The Waldensians were not accused of that -- that I know of. Then, even if accused, one would need prove the accusation.
That leads to mention of the Cathars and Albegensians.
Those were not identical to Waldensians, though there was some degree of overlap. The latter two were not even identical to each other, much less the Waldensians, although there may well have been a semi-pelagian aspect to *some* of the so-called Cathars, was it?
These things are difficult to establish, since Roman Catholics killed so many of them, there exists some documents which accuse, but when the parties themselves are allowed to speak for themselves -- then the accusations brought by Roman Catholic murderers are less than fully established (to say the least).
And I really don't think Waldo ever "came back' to the Roman Catholic Church.
You said that.
Now -- prove it, or retract that statement.
Meanwhile, read and learn -- before speaking.
Here's a good place to start ---->Schaff, History of the Church § 84. The Waldenses.
Other doctrinal developments added to the ascetic orientation in Waldensian ethics and demarcated them further from similar contemporary religious movements. First, Waldensians' views on salvation were characterized by a dichotomous soteriology and a semi-Pelagian understanding of how salvation could be achieved. The dichotomy in their soteriology--based on soteriological rather than metaphysical dualism--consisted of a strong belief in the existence of only two ways in life: the narrow path to salvation through Christ, in repentance and living according to this commands, and the broad way straight to hell. In its semi-Pelagian component, an emphasis on the human capability to choose righteousness and reject evil deliberately, Waldensianism stressed that it was in the here and now, in faith and in works, that every Christian could and had to choose between the two. While the semi-Pelagian component in early Waldensian ethics stressed the active pursuit of sanctification, the notion of the two ways made a Waldensian's moral probity in the process of achieving salvation all the more imperative. [1]
That leads to mention of the Cathars and Albegensians. Those were not identical to Waldensians, though there was some degree of overlap. The latter two were not even identical to each other, much less the Waldensians, although there may well have been a semi-pelagian aspect to *some* of the so-called Cathars, was it?
Nobody said they were identical and its disingenuous to suggest that they are being conflated. Semi-Pelagianism and Gnosticism are distinct heresies. The only reason to mention the Cathars and the Albigensians in reference to the Waldensians is in the sense that the Waldensians, in the beginning, were quite anti-Cathar and were initially dismayed at the Church's response to them. They believed the Church was not going far enough to suppress this heresy. The overlap occurs when the Waldensians begin to adopt some of the Cathar ecclesiastical structures.
Now -- prove it, or retract that statement.
I don't have to prove anything. However, I would suggest you review Waldo's Confession of Faith.
Meanwhile, read and learn -- before speaking.
I'm going to keep doing what I'm doing. If you have a problem with that then feel free to frequent some other forum.
[1] Kaelber, L. (1998). Schools of asceticism: Ideology and organization in medieval religious communities. University Park, PA: Pennsylvania State University Press.