To be more precise, Taney ruled that no state could give a black person any right of citizenship which would affect their status under federal law in any way. Most (if not all) states allowed free black persons to own property, enter contracts, and sue and be sued, and a few states even granted black adult males the power of suffrage. Taney did not seek to overturn these laws.
But he held that whatever a state might do, it could not make a black person a citizen in any manner in which a federal court could recognize. This contradicted at least two clauses of the United States Constitution, but Taney was satisfied.
The fact that slaves were non-citizens was not controversial in 1857. As others have said, they were property.
The fact that free blacks were non-US-citizens was controversial, or at least questionable, and “stateless persons” (under federal law) would be a good description of the resulting legal limbo. The concept, however, was less troublesome in 1857 than today. Nowadays we think of non-citizens as people who may not have a right to live in a particular country, and who may be deported. This was not so in 1857, when there were no immigration restrictions and non-citizens could happily live out their lives in the US. Taney no doubt lost no sleep over this problem.