Let's not exagerrate the scale of the problem here. While it is true that Stalin's base of support in the Red Army was the "Cavalry Clique", the one who really resolutely opposed modernization was Budyonny, who had a big voice because he was a civil war hero.
Ignoring that, the territory of the USSR favoured cavalry heavily, and this was helped by the offensive doctrine of the Red Army. In the civil war, where echelon warfare failed, it was up to the cavalrymen with their sabres to exploit breakthroughs and cause morale shocks. It worked, which is why the Cavalry Clique came to the forefront in the first place. And before the rapid industrialization, it was only a dream to convert all soviet cavalry corps to motorized units let alone tanks. By WW2 most cavalry usefulness was gone, but we should note that Italian cavalry managed to defeat a soviet force 3 times their size due to their cavalry patrols noticing the Soviet unit and giving the initiative to the Italians.