How can the hadiths that command dyeing white beards and the hadiths that command letting them grow be reconciled, given that both prohibit imitating non-believers, and dyeing is a Sunnah while letting grow is obligatory? And does this fall under the Sunan of Fitra?

There is no contradiction between the command to dye gray hair and the command to grow the beard. Dyeing gray hair is done by coloring, not by removing hair, and the command to grow the beard does not contradict this. Rather, both involve opposing the Jews and Christians. The command to grow the beard is obligatory, while the command to dye gray hair is recommended.