The Lone Star of Texas
Coahuila and Texas separated after they seceded and became independent republics. Texas now flew its own flag: Blue with a lone star in the center. Though this flag only flew a few years, it remains a Texas symbol and was used during the Civil War by the Volunteers of the Fifth Infantry Regiment, Hood's Texas Brigade.
In 1839 the current flag of Texas was adopted and was kept even when Texas gained American statehood in 1845. It too includes the iconic Lone Star of Texas.
So it's no surprise that by the 1860s, Texas cockades just naturally included stars!
Lone Star Cockades
The Ranchero noted on December 1, 1860, "Many citizens are wearing the blue cockade, surmounted by metalic five-pointed stars. The Telegraph notices the appearance of the blue cockade on the streets of Houston, worn by numbers of citizens, and gives the following descrïption of it: It consist of a neat blue rosette, pinned to the hat, having a silver five-pointed star in the centre. It means that the wearers pledge their lives, their fortunes and their sacred honor to resistance to abolition encroachments, and that they can see no way of successful resistance but in the withdrawal of their State from the Union."