Will a smaller tire size on the front than the rear cause the front wheels to get in a bind?

If this vehicle remains in 2WD then you will be fine.

However, anytime you put a 4WD with different size tires into 4WD then you are going to have issues.

On this transfer case, it will not bind immediately but you are going to damage the unit.

The reason is your input shaft and output are going to be spinning at different speeds and that is going to damage the unit.

However, if you remove the front drive shaft then you will never have an issue in case you forget.

https://www.2carpros.com/articles/how-to-remove-a-drive-shaft

Basically, you will be making this a 2WD truck and not have an issue.

Let me know if you have questions. Thanks