(I should preface this by saying that I play on a 3440 x 1440 monitor, which is ultrawide, or an aspect ratio of 2.39:1)

I am currently trying to decide which MDC (Monitor Distance Coefficient) value will allow me to have the most consistent mouse feeling across all games. 0% seems like it should be the best but many games seem to default to a MDC value of 133%. In games that don't have a Monitor Distance Coefficient setting, should I assume the value is 0%, 133% or something else?

No, you shouldn't assume that. Games only have a monitor distance coefficient when there is this formula used:

ADS Sens Multiplier = atan(tan((ZoomFOV*pi/180)/2) * Coefficient) / atan(tan((HipFOV*pi/180)/2) * Coefficient)

The only games that do this are Battlefield and CoD to my knowledge, and both use the vertical FOV for this scaling.

0% is not really a coefficient (multiply anything by zero and you get zero) rather just the focal length scaling formula, although the result is practically identical to some small coefficient value like 0.001 i.e this vs this yields the same result to 6 decimal places, and there are indeed a lot of games that use focal length scaling.

There are also other simplifications that end up with similar results to various coefficient values. Many games use simply a linear (ZoomFov*pi/180)/(HipFov*pi/180) which is the same as a coefficient of 1 unless you use different FOV measurements for each. For example, Doom Eternal does this but using the 16:9 horizontal FOV (therefore equivalent to 178% vertical coefficient), and CS:GO also does this but using the 4:3 based horizontal FOV. This is why CS:GO's sens scaling is said to be the same as BF USA / CoD Relative 133% default coefficient , even though it doesn't actually use the same formula or a coefficient at all. It just does ZoomFOV/HipFOV (see line 556) where the FOVs are the 4:3 based radians instead of vertical degrees.

There are also countless others than either use fixed multipliers so don't scale at all from hipfire FOV changes, or other calculations based off e or pi or anything else you could think of.

In any case, the best use for this type of scaling is really for ADS / zoom within a game from whatever your hipfire sens is. You are pretty much always better off using a hipfire sensitivity that works optimally for type of navigation movements you need to do in a given game. It would probably be a bit silly to insist on using the same hipfire sens in Quake as is optimal in CS:GO, given the completely different aiming movements required, and between similar games but where the FOV cannot be exactly matched then 360 distance still probably makes the most sense for hipfire so your navigation is familiar to what you are used to.

Some details that I should have included above about the settings I use:
Sensitivity: 

• 500 DPI
• 1.0 In-game sense on Source engine games
• WPS 6/11

which results in a 83.13 cm 360° distance. I try to match this distance in all of my games to help me build up muscle memory (I understand this is not optimal as you mentioned with the Quake example above but this distance feels good to me so far in all of the FPS games, it helps that I have an enormous mouse pad.)

FOV:

• Vertical FOV = 73.74°
• Horizontal FOV = 121.67°

I use this to match CSGO's 90° 4:3 FOV.

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Thank you for your fantastic answer,

My understanding of having 0% as the MDC value was that the sensitivity would be scaling to the very centre of the FOV, resulting in the game effectively "not using" an MDC and giving me linear mouse movement.

I am likely wrong in my understanding of this but I intereperated it from this image in the MDC explanation post:

My primary goal is to achieve the exact same mouse movement feeling in all of my games but it seems like that it is not possible because:

1. Not all games share the same default MDC or even have an MDC as you explained above.
2. Some games like CS:GO and DOOM do not allow the user to modify the MDC, preventing me from being able to set them to 0, so that they do not use an MDC.

Are these my 2 understandings correct? 

1 hour ago, Adam00 said:

1. Not all games share the same default MDC or even have an MDC as you explained above.
2. Some games like CS:GO and DOOM do not allow the user to modify the MDC, preventing me from being able to set them to 0, so that they do not use an MDC.

As long as the game support some sort of individual ADS and scope sensitivity, it doesn't matter what they use by default.

Obviously in games like CSGO you are limited to one zoom sensitivity, so only one aim can be truly 0%. But other games like PUBG (disregarding all the weirds ADS) you can still get MDV 0% for all the scopes even though the game uses MDH 100% bu default.