There is no penalty for publishing or sharing climate misinformation--which is the case in the U.S. for other kinds of disputed facts or opinions protected under the First Amendment's guarantee of free speech. Courts make very limited exceptions to this principle, mostly around statements that defame another party.
In 2016, California's legislature considered a bill imposing civil penalties for the spread of inaccurate or misleading climate information by businesses and organizations, but it didn't become law.