The main ingredient and most popular meat in BBQ, pork, was introduced by Europeans to the mew world and BBQ. That is a pretty fundamental contribution, really the most important one if you think about it.
American BBQ US a cuisine cultivated by Europeans as well as indigenous people and African Americans going all the way back to colonial times. It was a community event practiced at large celebrations, political rallies, and holidays. George Washington was a Big BBQ practitioner as we're other founding fathers. BBQ was practiced by all colonists even up to New England, so Caucasians have every claim to American BBQ legacy as others. African Americans definitely have a major hand in Southern BBQ because cooking was slave work, but only a small number of people actually owned slaves and BBQ's we're not only happening on rich southern plantations (and not even only in the south). So, while African Americans are big contributors, they did not invent BBQ or practice it exclusively. Whites we're there at the beginning, contributed their own sensibilities, and have been doing it as long as there has been an America and even before.
Additionally, "food appropriation" is a questionable idea as almost all food is aresult of trade, migration, war and conquest, and immigration, with veritably no cuisine being uniquely tied to a single nation historically.