Changing the order of line items (or what we call budget items) can be done on the EveryDollar mobile app. However, whole budget categories/groups (i.e. Giving, Savings, Lifestyle, Debt, etc.) can only be adjusted on the computer version of EveryDollar at everydollar.com. Click this link for more information:
Reorder Budget Items on EveryDollar.com
To reorder a budget item on the EveryDollar mobile app, simply tap two white arrows at the top right of the Budget view. 
Tap and hold the line item then drag it to reorder. Tap Save.
There is no function available to move a budget item to a different category/group at this time. You would need to delete the line item in the current group and add it again in the preferred group. The data would not transfer.