Are dyeing hair, growing a beard, and praying in shoes considered to have the same legal ruling, given the existence of Hadiths that prohibit imitating disbelievers?

Among the proofs that the ruling on changing grey hair and praying in sandals is not obligatory, unlike the ruling on growing the beard, is that there is a consensus that the command to dye grey hair is not for obligation. It is authentically reported that the Prophet, peace and blessings be upon him, prayed barefoot and in sandals, as did the Companions, may Allah be pleased with them. It is also authentically reported that the Prophet, peace and blessings be upon him, said: "If any of you prays, and takes off his sandals, he should not harm anyone with them; rather, he should place them between his feet or pray in them."