Should you avoid carrots on a vegan diet for to vitamin toxicity since even at 20 calories it puts you over 10000 iu?

Vitamin toxicity is extremely rare. Unless you're intentionally trying to poison yourself by overdosing on man-made vitamins. Carrots have water soluble Vitamin A, so you would pee it out faster than it could accumulate to poison you.

  Carrots are not unsafe to eat regardless of the dietary following. The beta carotene in carrots in the human body, also isn't converted easily into retinol. In the human body the conversion has an at best conversion of twelve to one. However that's at the optimal conversion. However not everyone's body is that efficient in converting beta carotene into fully formed vitamin A. In fact there are people whose body is incapable of converting beta carotene, into the fully formed vitamin A.

  Some but not all vegans and even some of those who are vegetarian are aware of that, and they're also among those who realize that there's no such thing as a one size fits all diet. Now back on topic, vitamin A is the number five for people being either low or deficient in. So no no one should avoid carrots in general, unless they have what could be a rare allergy to them or root crops in general. Which to the best of my knowledge, the only base type of diet that would tell you to avoid carrots as well as all other root vegetables are those following some form of a paleo diet.

Carrots are not toxic. And no one is going to eat 10 pounds per day for years. 

Carrots are not toxic. They are healthy and that applies to whatever diet you are on, omnivore or vegan or anything in between. I have them raw with salad as well as in cooked dishes.

Also, we NEED vitamin A. Read other correspondents answer for explanation.

The acute toxic dose of vitamin A is 25,000 IU/kg, and the chronic toxic dose is 4000 IU/kg every day for 6-15 months.

Carrots do not have a lot of vitamin A, but  they do have beta-carotene which is a precursor to  A. The body stops converting beta-carotene into active vitamin A  when you have enough vitamin A - preventing a vitamin A overdose.