Is it safe to use mouthwash that has alcohol when you have braces on?

Yes - But NOT Ideal! Alcohol based mouthwashes tend to dry out the mouth. A dry mouth is more prone to bacteria growth, which leads to increased cavities! a Fluoride mouthwash without alcohol will not inhibit saliva production. Saliva actually helps clear your mouth of bacteria and protects your teeth. Additionally, Fluoride will strengthen and protect your teeth while in braces!
Braces don't matter. Braces are unaffected by alcohol. The safety of alcohol in mouthwashes has come under question in general due to the suspicion that it may contribute to the occurrence of oral cancers.
Yes, but. Alcohol in mouthwashes will not affect braces, but don't use it as a substitute. Brushing removes about 3/4 of bacteria, flossing/WaterPik about 1/4, and mouthwash about 1%. Consider an alcohol-free mouthwash that contains Fluoride and follow package directions exactly.