Are you "entitled to your opinion"?
Not really - without reason or evidence it isn't an opinion.
There are a few terms that describe an opinion without reason or evidence:
Assertion: This is a simple statement that is presented as true, but without any justification.
Prejudice: This is a preconceived opinion about something that is not based on reason or experience. It's often negative.
Belief without reason: This term emphasizes the lack of justification for the opinion.
Hunch: This is a feeling or intuition that something is true, but it's not based on any solid evidence.
however climate deniers are slightly different
Denialism: often used in a strong sense, referring to the rejection of well-established facts and scientific consensus. It implies a deliberate attempt to disregard evidence, often for emotional or ideological reasons. For example, climate change denialism refers to the rejection of the overwhelming scientific evidence that human activity is causing global warming.
Also there is cognitive bias: This is a term that encompasses various mental shortcuts that can lead to biased thinking. Some cognitive biases can make people resistant to new evidence, especially if it challenges their existing beliefs.
For instance, confirmation bias describes seeking out information that confirms what they already believe and disregarding information that contradicts it.
If someone is simply resistant to new information due to mental shortcuts, "cognitive bias" might be more fitting. But if they are actively rejecting well-established facts, "denialism" is the stronger term.
Unfortunately along with the evidence most climate deniers are not familiar with these terms because they are unfamiliar with critical thinking methodology