Palm tree and crescent moon

Nikki Haley's photo shows her wearing a palm tree and crescent moon pendant.

This made me wonder: Was it a symbol of her Sikh heritage? a new age symbol?

 Nope. it is from the South Carolina flag:

The crescent moon on the flag of South Carolina were added as a tribute to the decorative crescent that was on the South Carolina military uniforms during the Revolutionary War; the palmetto tree was added during the Civil War as the South Carolina state tree. The flag was updated and revised several times before it achieved the design seen on the current flag.

photo courtesy Champion Flags

and a small correction: It is not a palm tree but a palmetto tree:

Nothing says South Carolina quite like the Palmetto tree. It’s on our state flag, and just about everything else across the state. South Carolinians unique love for the palmetto tree is a sense of pride that goes way back.,,

The palmetto is celebrated in historical significance dating back to the Revolutionary War. The British assault on Charleston on June 28, 1776 was denied by the thick palmetto walls of Fort Moultrie (called Fort Sullivan at the time). The walls were created by laying down large containment-forms of interlocked palmetto-trunks, then filling up their interior spaces to a considerable height with shoveled sand topped off with stacked sandbags. British cannonballs simply bounced off the dense mass of the palmetto logs. At that moment, a legend was born