Notions of "convergent evolution" and "degrees of freedom" fatally undermine your argument.
Culture has overwhelmingly more degrees of freedom than biology, which is constrained by needs to survive and also reproduce. Culture can sustain things like Scientology, Anime, and Froot Loops, in some places even simultaneously. Similarly, convergent evolution occurs only where environmental forces, such as a precise ecological niche, drive development into a very narrow range of possibilities with radically limited degrees of freedom.
In the total absence of any such constraints, the only viable explanation for detailed similarity across vast distances and dizzying time spans is common heritage.
Culture has overwhelmingly more degrees of freedom than biology, which is constrained by needs to survive and also reproduce. Culture can sustain things like Scientology, Anime, and Froot Loops, in some places even simultaneously. Similarly, convergent evolution occurs only where environmental forces, such as a precise ecological niche, drive development into a very narrow range of possibilities with radically limited degrees of freedom.
In the total absence of any such constraints, the only viable explanation for detailed similarity across vast distances and dizzying time spans is common heritage.