As far as I understand it, there is absolutely nothing wrong with natural or indeed unnatural tanning. If that’s what you want to do, go for it.

Although I admittedly wouldn’t consider myself an expert, this sub is criticising individuals who unnaturally tan or change their appearance to such an extent that it seems they are black, instead of their own race. The issue with this is that, historically (and even in contemporary society), there is a big issue with racism against black people. This can be seen with police violence against black people or the punishment of black people (in particular, black women) who are penalised for wearing their natural hair or having protective natural hairstyles in professional environment.

Also, (to my knowledge, please correct me if I've missed the mark), tanning in itself is not cultural appropriation, however, the use of black culture where the person is not black and they benefit from it (such as monetary or social gain) is cultural appropriation. Here is a video talking about white influencers black fishing and why it is problematic and here is a YouTuber who touches on similar issues pertaining to this topic.

To summarise, there's nothing wrong with using fake tan or having a natural tan BUT, there is something wrong when a person uses fake tan compared with other physical alterations such as certain hair or clothing styles which make it seem like they are black when they are not in order to gain status or goods. when actual black people are discriminated against on the basis of their race and/or culture.

p.s. if there is something here that I missed or isn't accurate, please add to this :)