If there’s a decent dribble there I’ll grab a paper towel or napkin and clean it off first, but I usually don’t worry about it. Wiping it off with a finger is disgusting though IMO. Her finger has about a thousand times more nasty stuff than anything in the sauce bottle, that’s a great way to contaminate an entire container.
The majority of the current ‘democrat’ party in the US are Neoliberals. Yeah it’s a right wing ideology, that’s the whole point of recognizing that even the ‘left wing’ here are still primarily conservatives.