Two lobbying groups for Big Tech companies such as Google, Meta, and Twitter have petitioned the U.S. Supreme Court to overturn a Texas law that forbids large social media platforms from barring users or censoring postings based on political beliefs.

Conservatives have long claimed that social media and other internet corporations participate in political censorship, which is why the measure was pushed by Republicans and signed by GOP Gov. Greg Abbott in September. The firms have consistently refuted the claim.

Instead, they claim to take action against users and content that violate standards aimed at protecting public safety, preventing real-world violence, and combating disinformation, among other things.

NetChoice and the Computer & Communications Industry Association petitioned the court for an emergency stay of the law, which allows site users or the Texas attorney general to sue firms if their posts are removed.

After a federal appeals court removed an earlier injunction, the bill took effect on Wednesday. The lobbying groups want the measure to be delayed again until lower court appeals can be heard.

The lobbying groups claim that the law forbids social media companies from "engaging in any viewpoint-based editorial discretion" and that it will "compel platforms to disseminate all sorts of objectionable" content, such as terrorist propaganda, hate speech, and posts that endanger children's health.

They also claim that the regulation will "fundamentally transform" the business structures and services of these sites.

According to the court that issued the last injunction against the bill, social media corporations have a First Amendment right to filter content on their platforms. The federal appeals court order lifting the injunction on Wednesday was released without the court's explanation, which the lobbying groups point out in their Friday petition.

"This one-sentence order explains nothing," says the filing, and thus "undermines the orderly appellate process" and hampers careful review.

In June, a federal judge blocked a Florida law from taking effect that would have allowed the state to punish social media companies for banning politicians or political candidates from their platforms.

The judge, in that case, found the law's prohibition on "deplatforming" may violate companies' free speech rights and said that the legislation on the whole is "viewpoint-based."

Friday's request for a stay on the Texas law was made with Supreme Court Justice Samuel Alito, who can rule on his own or refer it to the full court.