"Authority is the great suppressor of reason."
—Stephen Jay Gould

"Whenever you find yourself on the side of the majority, it is time to pause and reflect."
—Mark Twain

Whenever anyone makes any sort of claim, that person has a burden of proof. This means that the claimant must justify their claim with evidence or logical argument.

If you say "X is true", this statement can only be true if X is an observed fact or a conclusion resulting from a sound deductive argument. Most claims have no such justification so the claimants resort to logical fallacies to provide specious support. Two of the most common fallacies used in this respect are the appeal to authority and the appeal to consensus.

Argument from consensus fallacy (AKA appeal to the masses, bandwagon fallacy)

Truth does not change because it is, or is not believed by a majority of the people.

The appeal to consensus fallacy occurs when someone claims something is true because a large group claims it is true. But truth is not a popularity contest, it is irrelevant to how many believe it. The majority of people once believed the Earth was flat after all.

Argument from authority fallacy

The appeal to authority fallacy occurs when a person claims that something is true because an authority claims that it is true. But truth comes from reason and observation not proclamations from authorities.

Scientific authorities once claimed that animal fats were bad for you and that hydrogenated seed oils were healthier. We now know that hydrogenated oils cause far more health problems than animal fats ever did.

Argument from irrelevant authority

Many people falsely proclaim that appealing to authority is OK and the real problem is the appeal to irrelevant authority. The appeal to irrelevant authority occurs when you use an authority to support a claim but the authority is not an authority in the domain in question. For example, using the pronouncements of a renowned professor of physics to support the claim that Donald Trump is the next Hitler. The fact of the matter is that the proclamations of authorities, no matter how relevant they are, can never ever establish the truth of anything.

Some will combine the two fallacies to proclaim that something is true because the majority of experts in the relevant field believe that it is true. But no, it's still a fallacy for the reasons listed above. You can appeal to consensus and authority to make your own personal decisions but you can never ever use them to establish truth. You can only establish truth by observation and sound deductive logic. Science itself uses fuzzier inductive (or abductive) logic to provide approximations to truth but never ever truth itself.