Justin Timberlake apparently doesn’t mind his bad reputation. According to a source, the *NSYNC member — who is currently feuding with his ex Britney Spears — is unbothered by all the criticism he has received as of late. After the “Mirrors” singer publicly dissed his former lover during his January 31 concert, fans have been up in arms about his seemingly rude behavior. “If Justin comes across as cocky, he couldn’t care less. His conscience is clear,” the source said of the father-of-two. As OK! previously reported, the drama between Timberlake and Spears began when the pop princess painted t…