The law only disallows viewpoint-based censorship.
Twitter remains free to write and enforce an acceptable-use policy that disallows "bot-like" behaviors, as long as the policy and enforcement is viewpoint-neutral.
Twitter has no obligation under this law to disprove accusations of bias that arise due to disparate outcomes.
Furthermore, such a requirement would backfire spectacularly on the conservative right; consider all the other areas where disparity of outcome arises today.
What you're describing is possible would be a pretty big shift for Twitter and would make it simultaneously less pleasant and less useful. Under the policy you propose that would comply with the new Texas law, a bot that automatically posts new state regulations as they come into effect would be banned, but human Nazis could freely advocate for ethnic cleansing.
Twitter remains free to write and enforce an acceptable-use policy that disallows "bot-like" behaviors, as long as the policy and enforcement is viewpoint-neutral.