I've heard it mentioned that removing red meat from my diet would cut more carbon emissions than giving up my car - is this true?
It's not about your diet as much as it is the farming of the meat.
According to this article in the Guardian:
The heavy impact on the environment of meat production was known but the research shows a new scale and scope of damage, particularly for beef. The popular red meat requires 28 times more land to produce than pork or chicken, 11 times more water and results in five times more climate-warming emissions. When compared to staples like potatoes, wheat, and rice, the impact of beef per calorie is even more extreme, requiring 160 times more land and producing 11 times more greenhouse gases.
Red meat needs much more land and water, and produces more emissions than both other meat and vegetables.
It's not that you are producing more carbon, it's the meat being farmed.
But yes, if the whole world were to give up cars and give up red meat, red meat would have a bigger effect. It's hard to say on a personal level, it would depend on your car and how much red meat you eat.
Below is a table comparing the carbon footprint of common foods versus driving. For example, the first entry of 91 in the column titled,
equivalent miles driven / kg, means that eating 1kg of lamb has the same carbon footprint as driving 91 miles. The 16 in the column, to the right, titled,
equivalent miles driven / 500 cal, means eating 500 calories of lamb has the same carbon footprint as driving 16 miles (some foods have a lot of calories per unit mass, so I included both weight and calorie measures for the quantity 'amount of food').
Food equivalent miles driven / kg equivalent miles driven / 500 cal
Lamb 91 16 Beef 63 13 Pork 28 6 Cheese 31 4 Chicken 16 3.5 Eggs 11 3.5 Milk 4 3.3 Rice 6 2 Fruit 2.5 1.4 Lentils 2 0.8 Beans/tofu 4 0.7 Nuts 5 0.5
The average American consumes 90 kg (or 200 lbs) of meat per year. So if we assumed that was all red meat and replaced it with chicken, we are going from 5,670 miles/year to 1,440 miles/year. So switching red meat for chicken is approximately equivalent to a 4,230-mile reduction in driving (in terms of carbon footprint). The reduction of going from red meat to chicken is huge in comparison from going from chicken to vegan.
The average car owner drives about 16,500 miles per year. So switching from beef to chicken saves about one quarter the impact of ditching your car. Of course, if you eat more meat or drive less it could very easily have a greater impact.
It should be noted that carbon footprint isn't the only form of environmental impact. These calculations are only for carbon. Both driving and eating meat have other effects on the environment. Meat especially requires water, land clearing of land, and produces other greenhouse gasses such as methane. These effects are likely much more harmful to the environment than the carbon impact but thought I'd include the above analysis anyways to add some concrete numbers to this answer.
*The table is based on these sources Food / Car Miles Equivalent per kg consumed (only from carbon emissions does not include other environmental impacts such as methane, land clearing, and water usage, etc.). Per 500 cal sources done by computing the calories for that item using google's calculator. The table is sorted by the last column because I think calories is a more useful unit of comparison than mass.
I'm not sure about the relative decrease in comparison to driving, but I found this study suggesting that a vegan diet on average cuts your green house gas emissions in half: Scarborough
In conclusion, dietary GHG emissions in self-selected meat-eaters are approximately twice as high as those in vegans. It is likely that reductions in meat consumption would lead to reductions in dietary GHG emissions.
As @easterly-irk pointed out, it's difficult to say if your individual meat consumption is having a bigger impact than your driving.