There are a few things that need to be clarified, because they're all fairly distinct even though they might seem to be doing similar things:

• Copyright: protects the reproducibility of some work. Objective: a time-limited monopoly for the owner to control copies

• Trademark: protects the authenticity of a vendor. Objective: elimination of marketplace confusion; vendors are judged on their merits

• Patent: promotes disclosure of innovations and protects the use or application of an invention. Objective: a time-limited monopoly for the owner to control uses, but must disclose the secrets for how to build it

• Defamation: (USA specific) protects against provably false statements published about someone. Objective: elimination of lies from the marketplace of ideas, but does not affect opinions or public mores

• Right of publicity: protects personal marketability and opportunities. Objective: elimination of labor marketplace confusion; person will be judged on their merits

There are two things which can cut against almost all of these: fair use and parody. Fair use arises commonly in copyright but the logic is the same: in order to discuss something, the thing must be identified. The marketplace of ideas cannot exist if nobody was allowed to screengrab a TERF's wizard movie or mention why they don't like a certain cola company. The key is to be minimize the incursion to what is absolutely needed. For example, someone organizing a boycott can indeed use a brand's logo to refer to that brand.

As for parody, it goes a bit further and will (for comedy or sarcastic intention) assert that the statement is true or the work is authentic. This too is allowed, because -- at least in the USA -- poking fun at things is a valid (and human) way of discussing things that would otherwise be difficult to say. How it relates to defamation, trademarks, and right of publicity is that a reasonable viewer of the parody must be able to determine that yes, it's a joke and it's not actually making that particular point but rather a different one. This is akin to someone nodding their head to say yes but verbally saying "no": there are enough mixed signals that nobody would take the assertions seriously.

So would someone's face be "locked out of the arts"? No, not by copyright. But under right of publicity, they could have a claim if the depiction could potentially be confusing. Fortunately, this generally can be cleared up by explicitly identifying who the depicted face belongs to. And also to never try to sell or distribute artwork that rides on that person's coat-tails.