Matthew 10:9-10
9 Provide neither gold, nor silver, nor brass in your purses,
10 Nor scrip for your journey, neither two coats, neither shoes, nor yet staves: for the workman is worthy of his meat.
Luke 9:3
3 And he said unto them, Take nothing for your journey, neither staves, nor scrip, neither bread, neither money; neither have two coats apiece.
Mark 6:8-9
8 And commanded them that they should take nothing for their journey, save a staff only; no scrip, no bread, no money in their purse:
9 But be shod with sandals; and not put on two coats.
The assertion is that Matthew and Luke have Jesus forbidding the carrying of staves, but Mark commands it. That's not correct. Read carefully - both times Christ says not to take a staff, it's plural - staves.
In other words, He's commanding them not to take any surplus on the trip, in order to trade or what have you. They are allowed to take one pair of sandals (Mark 6:9), not multiple shoes (Matthew 10:10). Similarly, they aren't supposed to take two coats.
This is a commandment against them taking surplus, and there are multiple valid ways to paraphrase what Christ said here. These do not contradict one another at all.