The main people who say its racist are liberals. I have noticed its part of the liberal narrative to attack anyone who is conservative, votes republican, white, christian etc. is incredibly racist. Part of the reason I am no longer liberal is because I couldn't stand all the liberal talk shows I watched, like the young turks, constantly trying to make me feel guilty for being white.
Texas naturally gives liberals butthurt because it is very conservative, very christian, has been solidly republican since the late 90s, likes guns, and is white (It's actually only 45% white, but it's stereotyped as being majority white by a lot of people, probably because it's a very red state). The icing on top of the liberal butthurt cake however, is that Texas is a very red State and it's very successful.
The only other state you could probably compare Texas to in terms of population and economy is Commiefornia, one of the bluest states in the nation. Compare the two, and Texas usually comes out better. Texas has lower Taxes than Commiefornia, it has better education (only a few ranks higher, but we spend a lot less for it). Stuff generally costs less in Texas, especially land. The percentage of people in poverty in Texas is lower than in Cali (source: Supplemental Measure of Poverty). I think Texas's success makes lots of Liberal intellectuals, journalists, and entertainment creators mad so they feel like they have to take it down a peg every chance they get. Most stories about Texas that I read that make the national news usually have a negative slant, or appear to only make national news cause it makes Texas look bad. They often time bring up our past as a slave and segregation state in order to draw parallels to certain laws Texas enacts that they don't like.
Now there is racism in Texas, you will find that in any State. However, it's usually just unflattering opinions or slurs about certain races from some people. Most people I see in Texas try to be polite as possible regardless of race. They will not attack you or harass you for being gay or being black, or muslim or whatever. I don't give a fuck what race you are, as long you treat me kindly, and I have pretty /pol/ tier views on race. I'm in a more conservative area than Austin, and even the Rednecks don't seem to be that racist, if at all. People are generally kind as long as you treat them kindly.