In a country like Vietnam or Japan (or when applied at an individual level rather than a societal level, each individual weighing whether they actuall need more exercise at the moment) we can get back to the simple assumption of walking requiring extra calories (which you'll eventually eat due to hunger and some sort of weight homeostasis) and just running the numbers (all slightly conservative for "typical" scenarios, favoring beef over gasoline to mildly steelman the argument):
- Beef produces something like 48 lbs of CO2 equivalent emissions per pound
- Beef is something like 1200 calories per pound
- Walking burns something like 90 calories per mile
This directly gives 3.6lb of CO2 equivalent emissions per mile. Under a homeostasis assumption, none is sequestered on average long-term in the person doing the walking, though actual emissions could be slightly higher or lower when taking into account the relative greenhouse impact of human emissions in response to that digestion/exercise (but this is somewhat negligible compared to a cow's methane production).
Even pretty crappy cars in city driving conditions can achieve 20mpg, which is only 1.02lb of CO2 equivalent emissions per mile, 3.5x better.
Most people aren't eating pure beef, but the break-even point (compared to that hypothetical extremely shitty car; the argument favors gasoline even more with more modern vehicles) is 28% of your calorie budget (assuming all other inputs have zero greenhouse impact).
Chicken is better at only 1.6lb of emissions per mile of walking, with a break-even point at 63%. Cheese and butter are _slightly_ better still. Nearly all animal products are much worse than gasoline, and basically any diet made from >=70% animal products (denominated in calories) will have higher emissions than a 20mpg car and driving habit.
If you compare it to more typical cars (my car is dirt cheap, from 2008, and still gets 30mpg city even after 17 years of wear and tear), the break-even point is much worse.
Counter-arguments include that the carbon impact of a car is much higher than just its gasoline consumption, but if you work through the math everything else put together is a rounding error compared to the gas over the lifetime of a vehicle (still 5-15%, but it doesn't substantially impact anything I've said so far).