“Why are the accounts of the Anointing at Bethany so different?”
The Short Answer:
The accounts of the anointing at Bethany are not that different at all. If you mean to add the anointing that happened in Galilee to this, then yes, they are quite different. But that’s a different anointing then the one at Bethany. Since I’m not sure what you are thinking, I’ll address both!
The Long Answer:
All four Gospels record a woman anointing Jesus’ feet. What you appear to be assuming with this question is that these are the same event. While they are similar, it’s the differences you refer to that cause us to conclude that this foot-anointing, in fact, happened to Jesus on two different occasions.
Why Two Events?
The event (& woman) in Luke 7:36-50, must be a different event (& woman) than the one mentioned in Matthew 26:6-13, Mark 14:3-9, and John 12:1-8.
The first occasion (recorded in Luke) take place in Galilee, while the second (recorded in Matthew, Mark, and John), takes place in Bethany.
The first occasion has the woman remain unnamed, while the second occasion names her has Mary, the sister of Lazarus (at least, she’s named by John).
The first occasion has a Pharisee objecting to the woman’s act of devotion. The second occasion has either, “some who were there,” or Judas, or the disciples reacting.
The first occasion has the woman weeping over her many sins, which Jesus forgives her. The second occasion, Jesus tells us, was Mary, who loved Him, anointing Him to prepare Him for burial (which would be in two days).
Jesus’ words in the first occasion (Luke), are different than in the second occasion (Matthew, Luke, and John).
Why are Matthew, Mark, and John the Same Event?
That is why we conclude there are two separate anointings. Now, why are Matthew, Mark, and John considered the same? Because Luke has details that contradict Matthew, Mark, and John… but while Matthew, Mark, and John (the Bethany anointing) have differing details, they do not contradict one another (and in fact, largely agree with each other).
Again, the location (Bethany), and Jesus’ own words are similar in these three. But what about the differences in John? John tells us Mary’s name, and mentions that Jesus arrived in Bethany 6 days before the Passover (when He would be crucified), and mentions that Martha helped serve the meal—Matthew and Mark do not. The answer is simply: These are additional details John adds to Matthew and Mark’s version, but importantly(!) they do not contradict anything from Matthew and Mark. And we can work it out, so for example: Jesus arrived in Bethany six days before Passover John says, but this meal was still held two days before, not six (as Matthew and Mark say). The meal was at Simon the Leper’s house (as Matthew and Mark note), but Martha must have helped serve at Simon’s house (this is the Martha we know, isn’t it?). And more: The different people who are said to respond: Judas, the disciples, or “some others”… are again, just different details, but provide no contradiction. There was obviously a reaction from everyone in the room, as we might expect. The fact is: The authors of the Gospels will record the same event, but with different details. Sometimes this is an important part of the message they are trying to convey.
So Matthew, Mark, and John we can conclude are the same event, and Luke is different.