The fundamental flaw in the best intentions of “equal parenting” is the child. Turns out the kid has some intentions too.
Lots of planned ideas – it’s mommy’s turn for diaper change; we’ll take daddy’s car to the supermarket; daddy will read you a book tonight; mommy gets to sleep in this morning – turn out to be a lot less important than you thought once a child starts weighing in with their own thoughts.
So the rule of thumb is that equal parenting is a noble goal, but be sure you’re balancing that equality across all three of you, not just the parents.