The Institute on Taxation and Economic Policy thinks so. They rate Texas as the second most unfair taxation policy in the country, with the lowest 20% of incomes paying 13% of their income in taxes, over two percentage points higher than in California.
In fact the only ones who do better in Texas are -- to the surprise of literally no one -- the top 1%.
The only source I could find that tried to argue differently was The Tax Foundation, which is primarily founded by corporate interests including the Koch Brothers and has a history of advocating for right-libertarian economic policies.