Is there any way to speed up actions in XCOM 2?

In addition to Stop Wasting My Time (made by a very mysterious and handsome author) already mentioned, there are a few other time-saving mods I highly recommend:

• Instant Avenger Menu: Instantly move between rooms in the Avenger. Also speeds up Avatar Project updates.
• Evac all: Adds a button to evac all units at once, rather than having to do it one-by-one
• Overwatch all: Same, but for Overwatch.
• Strip Primary Weapons: Adds a button to remove all weapons from all non-mission soldiers before a mission.
• If you like to color-code your soldiers by class, Automatically Color Units or Character Pool Uniforms will save you time.
• No Startup Movies: Skips the movies at the start of the game, speeding up the initial load time.
• Always Show Shot Breakdowns: Saves you from having to click the left-arrow on the attack screen all the time (which is actually a bug)

Also, the "experimental mod" mentioned by the other answer, Ignore Missing Content Warning, allows you to force-load a save game created with mods that are no longer installed. You wouldn't want to do this with any mods that add actual content (new flags/models/weapons/classes etc.), but all of the mods listed here should be togglable at will.

Not in-game actions, exactly, but there's currently an undocumented feature that lets you skip loading times after missions (i.e., the ones where everyone is sitting on the dropship heading back to base) just by pressing Caps Lock.

"Hitting the key, through a Rube-Goldberg-esque series of events, forces all outstanding load requests to be filled immediately in a single frame. This causes a massive hitch, and potentially could crash the game. If you don’t care about those adverse effects the synchronous load is faster." (developer at Firaxis)

I tried it last night, and it did shorten the loading to a couple of seconds. Just be aware that, as Firaxis says, this could possibly crash your game, so make sure you have autosaves turned on if you do this.

Incidentally, I found out about this while searching for information on the Lock and Load continent bonus, which I hope becomes the official name of the feature.

There is now an official solution to this as part of the latest Xcom2 patch without needing to use any mods:

Players can also opt into the new “Zip Mode” option by pausing the game at any time and activating it under gameplay options. Zip Mode will create a faster paced experience that speeds up animations and some delays in gameplay.

Another tip is you can press "tab" while moving a soldier, to switch to another solider during the action. This means you can quickly have 3-4 people moving "simultaneously" across your map. However if you try to press tab, and it doesnt work during a specific soliders action, it is because that soldier is about to trigger "something" (i.e. a pod, a voice script, a civilian running - anything).

CheatEngine's Speedhack feature works pretty well in XCOM, I usually have it on at 2x speed. (I've tried Stop Wasting My Time, but the effects seem pretty minor.) It basically has the effect of running the game loop at the chosen modifier, so all animations run twice as fast.

Sounds aren't affected, which is mainly a problem in cutscenes, which will get massively desynchronized. CheatEngine has hotkey support, so it should be possible to set up a toggle to disable the speedhack in cutscenes.