Why is ゟ considered obsolete? I recently discovered the kana , which is a ligature of and , so it's the comparison particle. According to a few sites it's obsolete, or 'dated'. Why is considered obsolete, and why should I use it, or avoid doing so?

The reason is very simple: universal education.

is not a "kana" but an abbreviation () used in the 1800s. In other words, it is not an outdated letter like long s (ſ), but a scribal abbreviation like "Ↄ̄" for " _contra_ ". It was mainly in use when writing was limited to a small literate class, and when language began being taught to the public at large, it was omitted, as can be seen in this 1874 textbook.

Wikipedia says that you can still see in newspapers from time to time; I might have seen it myself at some point. But the most common scribal abbreviations still in use today are the iteration marks , , and . You should not use the other ones.