That is not true at all. Race has no bearing on whether someone is or is called a thug or not.
Unfortunately this is not true at all. The word "thug" became popular in the hip hop culture when rappers like 2 -Pac coined the phrase, and invented an all new culture called thug life. Young black males began to embrace being called a thug, as rap song after rap song was released, which embraced and glorified violence, drug dealing & use of drugs, and total disrespect and disregard for women and society in general.
After a few years, it became pretty common for many people who wanted to describe a black male in a negative light to call them a thug. Ignorant people on sports boards have called Adrian Peterson a thug, Blake Griffin, and other athletes who had no thug traits, other than they have darker skin and may enjoy rap music.
The greatest fault, IMO was the black community embracing the word. It became common for people to use it in the same ways the N-word is often used. There are tons of very well written educational pieces on the internet, and some published work in several credible magazines that describe thug as the new N-word.
It is very common for white people who have never embraced the hip hop culture, to see a young black male who APPEARS to be trouble, and immediately they call him a thug. Most black athletes who run afoul of the law, or show blatant disregard for what is considered appropriate behavior, are called thugs, even when there is no real evidence to support that. Richard Sherman is a good example.
As a black man I don't blame the white race for the popularity of the word. Hip hop made thug life attractive to young black men, and now the word and culture carries a negative connotation, and it is usually used to describe blacks and even hispanics who are considered less than desirable. Because of this, many athletes and young men of color are unfairly called thugs, without any evidence of them being a thug.