Muslims do not worship the Kaaba nor do they worship the black stone set within the walls of the Kaaba. Muslims worship only God (Allah) alone. No partners, no children, no parents, no symbolic representations, etc... just God.
The Kaaba and the black stone have great significance to Muslims but are not worshipped. the black stone is believed to have been sent down from heaven to mark the spot where God wanted Adam to establish an altar for worship. When it first came down it was supposedly a brilliant white but over the centuries the stone turned black from absorbing the sins of the people. The stone remained in that spot and eventually Ibraheem (Abraham) left his wife Hagar and his son Ismail (Ishmael) in the desert they lived in the same area that this stone was originally sent. Ibraheem didn't just abandon his son there and never return he came and visited from time to time and on one such occasion Allah revealed to him the location of the stone and Ibraheem and Ismail together built the first Kaaba in that spot and set the black stone into the wall. Eventually over time the people in the area began to worship other than Allah and added idols to the Kaaba. Before Muhammad (SAW) became the Prophet the Kaaba had suffered a fire which had damaged but not completely destroyed it. The Meccans renovated the building and cleaned it up, placing the black stone back into the wall. It was damaged twice once in 683 and again in 952. The damaged pieces are joined together by silver ligaments and a silver frame covers them holding them in plae in the wall. Touching, kissing, or at least reaching towards it is part of the Hajj ritual. So while it is important historically for Muslims and is one of the many parts to the Hajj ritual it has no worship. In fact when it was removed from the Kaaba for a time pilgrims simply continued on with their worship and pretended it was still there or touched/kissed/reached for the place it once was.
Do Muslims worship the Kaaba or the black stone? - Quora