$hat{phi}$ tidal acceleration of a black hole

For Schwarzchild geometry I’ve calculated the tidal acceleration in the $hat{phi}$ direction for two particles initially at rest separated by $Delta phi.$
$$a^a = -R_{cbd}{}^aX^b T^c T^d$$
Where $X^b = (0,0,0,Delta phi),$ and $T^c = left(frac{dt}{dtau}, 0,0,0right).$
This gives
$$a^3 = -R_{030}{}^3left(frac{dt}{dtau}right)^2 dphi = frac{-ME^2}{r^3 left(1-frac{2M}{r}right)} Delta phi.$$

I’m next asked, given the tolerance of the human body, what size of a black hole could a human survive when crossing the event horizon. But this predicts an infinite tidal acceleration at $r=2M.$ (Notice that this is different than the usual problem of calculating the tidal acceleration in the $hat{r}$ direction, in that case there is no divergence at $r=2M$).

So what is going on here? Have I just miscalculated $a^3$?