This is pretty misleading. The report in question doesn't say whether Texans or California's actually pay more per capita - it's entirely as a percentage of the total state tax collected. https://itep.org/whopays/ (EDIT: This isn't correct, it's as percentage of income by average income in state, but the brackets are different per state).
So it's because they are missing an income tax. But if someone hit you with a 50% income tax next year, you wouldn't consider your tax bill lower just because your share become proportionally smaller.
With that in mind, per capita tax in California is ~$6800 and in Texas it's $4400.
FWIW, I've never actually heard anyone complain about state taxes in California or consider moving because of them. The exodus to Texas has less to do with taxes and much more to do with general cost of living, which is still largely a function of state government.