Requires the library mod Collective.
This mod is part of The Vanilla Experience.
Move Minecarts is a drag-and-drop mod which allows players to easily pick up and move minecarts without breaking them by holding right click.
You may also be interested in Move Boats.
Configurable: ( how do I configure? )
mustSneakToPickUp (default = true): When enabled, will only pick up the minecart when the player is crouching and holding right-click.
To pick up: Hold right-click and crouch while looking at the minecart. You can release the mouse button while moving the minecart.
To release: Right-click the minecart again.
Here you can see a minecart being picked up; be careful with a tnt cart!
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You may freely use this mod in any modpack, as long as the download remains hosted within the CurseForge ecosystem.
Serilum.com contains an overview and more information on all mods available.
Comments are disabled as I'm unable to keep track of all the separate pages on each mod.
For issues, ideas, suggestions or anything else there is the Github repo. Thanks!