The SBC is to the right of Bernie Sanders. For example, it prohibits male pastors and says the husband is the head of the family and the wife subservient to him.
They define 'alt-right' as a synonym for white supremacy, thusly: Racism and white supremacy are, sadly, not extinct but present all over the world in various white supremacist movements, sometimes known as "white nationalism" or "alt-right" - http://www.sbc.net/resolutions/2283/on-the-antigospel-of-alt...
Therefore, your description about this being a tactic of the left doesn't hold water.