It's not a retcon that bothered me. When I saw Dru turn Spike in Fool For Love, it immediately clicked with me. It felt right with the dynamics between Angel, Spike, and Dru is S2. That it contradicted a one-off line from Spike in School Hard did not bother me - I had been a hardcore fan of Marvel Comics a couple years earlier. Marvel comics have been rife with continuity errors since they were first called "Marvel" - and probably before, but I haven't read much of the Atlas or Timely days. I had at that time, and to some extent still do, a high tolerance for continuity errors.
(Oddly, in my days of exploring comic book fandom I found many Marvel and DC fans who took minor continuity errors as a sign that a writer of a title was unworthy. As if the writers they respected never made errors like that. I've seen this attitude again in Supernatural fandom, where major continuity problems in the earlier seasons are ignored, while even minor continuity problems in the later seasons are presented as proof of sucktitude.)
However, the oddest thing is that while the Fool For Love contradicting a single line from an earlier episode has gotten a great deal of discussion, a far deeper, more subtle, and in some ways just as long-reaching retcon made sometime during Buffy S3 or AtS S1 is usually not even noticed. In fact, I'm not even sure I can point out exactly when it happened.
In Innocence, when Dru realized that Angel has lost his soul, she doesn't exclaim, "Angelus". She exclaims, "Angel". And Angel replies, "Yeah, baby. I'm back." As if it were perfectly naturally and normal for his soulless self to be referred to as Angel. Throughout S2, the Scoobies call Angel "Angel", whether souled or not. In Becoming Part 2, Spike talks about wanting to stop Angel from destroying the world - not Angelus. Never at any point in S2 is the name "Angel" treated as a name only for for souled "Angelus" - it's just a shortening of Angel's more formal name, usable for either souled or soulless.
As I said, I am not sure when this retcon first happened. I didn't notice it at first - in fact, I still have a moment of surprise when I watch episodes and read transcripts, and see that S2 "Angelus" was not "Angelus" at all. All I know is that in BtVS S2, Angel didn't go by a different name when he was soulless. In AtS S2, he most certainly did. When and where exactly that change happened I couldn't tell you.
The retcon that Drusilla was Spike's sire is a change of physical fact. Angel/Angelus is simply an act of naming. The former does at first glance seem far more significant, even if we had no evidence for this fact aside from a one-off line by Spike.
But the Angelus retcon affects more than just the way characters word things. AtS S4, which treats Angel and Angelus as two separate beings, demonstrates how a simple matter of name can extend to physical facts. If Angel was only called Angel, that portrayal would have been difficult if not impossible
Angel is most believable as a character when he is aware that there is no undeniable line between who he is with a soul and who he is without. Angel/Angelus makes it easier both for him and those around him to deny it. One of the most frustrating things about Angel for me was the way the writers would let the horror of the full implications of Angel's dual identity out of the box...and then firmly stuff it back in again. Buffy S2, especially Passion, made a lot of the similarities between Angel and, uh, Angel. S3 promptly proceeded to put it on the backburner for Angel's own show, which meant his romance with Buffy throughout the season became repetitive, offering nothing new to say. AtS S2 dealt directly with the reality that Angel is Angelus, but that, too, was dropped, and two seasons later we have a storyline where Angel actually loses his soul for the first time since Innocence - and it ends with Angel stating as an accepted fact that he is not responsible for Angelus' actions, which flies in the face of the one of the few consistent themes of the show: Angel's redemption.
With Spike's arrival, S5 does a better job of addressing Angel's soulless self as, in fact, himself. But it's not enough to make up for years of inconsistency and cop-outs.
Referring to souled and soulless Angel by the same name would not solve all the problems of how the character was portrayed, but it would, at least, have made cop-outs more difficulty. It would have made it harder for Angel, those around him, and the narrative itself to deny what he is.
And oddly, it's a retcon that is not treated as one - not by the show, and not by most of the fandom. I took a silly quiz once asking you to identify whether certain quotes were made by Edward Cullen and Angel. One of the quotes I recognized immediately as spoken by soulless Angel in season 2 of Buffy. I chose Angel as the answer - the quiz told me I was wrong. The correct answer was Angelus. In season two. Where everyone called him Angel. This is par for course in my experience for how fandom talks about Angel.