Not the OP, but I have some feelings about that. The limits on trademark law are much more fair, in terms of the balance afforded to the public and the limited monopoly granted to the rightsholder. Trademark law can be abused, for sure, but it hasn't been used in the same abusive way as copyright law, nor has it expanded to be functionally infinite and all-encompassing.

I think the creative part of trademarks should be free to use, e.g. a film can have Coca-Cola bottles or some corporate mascot. But if you are commiting fraud, e.g. by labeling a Coca-Cola bottle, not from the company, as such then this should be forbidden. Not on the basis that Coca-Cola has any right to be the only ones using their logo, but that customers have a right to not be defrauded and make choices from whom they buy. As long as the trademark is not used to defraud people it can be used however people want.

Someone's identity, e.g. their likeness and identification aren't just ideas. They actually physically exist. (I assume here that by identity you don't mean how they view themselves). For identities I think it is very important to consider publication. If you publish something you have no right to tell others what to do with it. An actor in a movie has no right to tell someone that their fan cut of a movie is not allowed to exist. On the other hand, as long as you do not publish some part of your identity you should have a right to it. If you are recognizable on a photo that you do not want to have published it should not be published.

To make it short I essentially agree with the GDPR, with the exception of being able to retract consent, but I do not believe it invalidates my stance on IP in any way. Your likeness is not an immaterial idea derived from a creative process, neither is your own house address. You should be allowed to publish it and by publishing it, that publication is no longer yours to own and control.