If you're working with a symmetric model, keeping its UV map and texture symmetric is a good idea. This add-on can detect the structure of your mesh and adjust each UV vertex automatically.

Symmetrize your UV map

If your UV map should be fully symmetrical, just use the Symmetrize function. This function makes the UV map symmetry across the specified axis on the panel. 

You can use a brush ("Start Brush") if your mesh has some asymmetrical parts. When you trace some parts with the special brush, the only traced parts are symmetrized. The size of the brush can be changed by pressing the "F" key.

Expand mode

The Expand mode is a feature that creates a double-sided UV map from a single-sided UV map. You can also use a brush if needed.

Position the axis anywhere

The axis of symmetry can be placed anywhere by using the 2D cursor as a pivot point. You can specify one from Center, Start, End or 2D Cursor in the "Axis Position" option.

UDIM tiles supported

Symmetrizing is performed based on the UDIM tile boundaries when working with UDIM texture (if "Use Tile Boundary" is turned on). You can now efficiently symmetrize UV maps on each UDIM tile.