Is worshiping the stone a pre-Islamic tradition? If so why are Muslims practicing a pagan tradition?
I am not sure know which commonality you're referring to here because Muslims evidently do not worship stones, but you might be referring to their respect for the dark stone at the corner of Kabba which muslims similar to pre-Islamic pagan Arabs consider sacred.
For the why of this, you should note that pagan Arabs were originally the descendants of Ishmail, son of Abraham the founder of the Monotheistic faith that continued into Judaism, Christianity and Islam. So many of these pagan Arab rituals had been intuitively rooted originally in rituals of Abrahamic faith. But as evidenced by history and Islamic narrative some of their originally valid monotheistic rituals had become over the course of time corrupted by non-Monotheistic human distortions and alterations. Therefore an important task of Prophet Muhammad like all past prophets had been to restore these adulterated religious rituals back into their pure Monotheistic version.
Another important point is that according to Islam, even among Pagan Arabs, there have been a steady line of monotheists who kept true to the original unadulterated version of Abrahamic faith and were therefore wary and disapprove of these pagan beliefs and practices that had influenced the Ishamalite Arabs over the course of time. Prophet Muhammad himself was the last in line of pre-Islamic Arabs who adhered the original Abrahamic traditions and were critical of polytheistic influences and moral decline of the Arabs.