I believe that the philosophical divide in the speedrunning community is actually between tool-assisted speedruns[1], and unassisted speedruns.

[1]: https://en.wikipedia.org/wiki/Tool-assisted_speedrun

There doesn't have to be only one divide.

Most TAS communities have different categories for glitchy and non-glitchy runs. Take a look at http://tasvideos.org/ for examples.

I don't know any serious speedrunners who consider most exploits to be cheating. Something as simple as bunnyhopping is an exploit, yet you'd be laughed at if you tried to run Quake without doing so.

True, there are some exploits which are truly degenerate, but they are specifically handled. Exploits in general are highly encouraged. Speedruns are listed in terms of the restrictions given: a specific difficulty, 100% vs any%, rules governing the timing, etc.

Skiing in Tribes was originally a bug, and it became an essential feature and set the franchise apart from other shooters.

Exploits in speedrunning aren't often easy to do, and finding new applications for them are part of the challenge and can set one speedrunner ahead of another.

I remember seeing a speedrun of Half-Life where the player went through a wall (that you weren't supposed to go through), kept going (past all of the weird clipping visual nonesense), and finally came out in a different level (which IIRC wasn't even populated with enemies), and kept going through the game.

That seems like cheating to me. Little glitches in the game mechanics are a little bit different.

The problem is that there's no bright line to be drawn between bunny hopping and glitching through a wall. It's a continuous spectrum of larger and larger glitches.

Just out of curiosity, I assume you'd also consider abusing the "minus world" glitch in Super Mario Bros to be cheating, assuming it happened to let you finish the game faster? That glitch is nearly identical to the Half-Life case you described.

Bunnyhopping is allowed, but the problem was that for one Half Life run macros and authotkey was used to sequence things. Bunnyhopping using only mouse, keyboard or gamepad is okay