I've been ruminating a post on this recently because Charlie prefers Mr. Bee while Olive prefers me. In day to day life it's not a big deal and both kids are fine with either parent. But it is a challenge at bedtime and in the mornings sometimes.
Since Charlie is older and I can reason with him, when he does ask for Mr. Bee at bedtime, he is generally fine. Olive asks for me at bedtime often, but sometimes she cries pretty hard. She also asks for me if Mr. Bee gets her in the mornings. She's much harder to reason with because she doesn't understand.
I've done Olive's bedtime since she was born, while Mr. Bee has done Charlie's bedtime since she was born. The reason we switched recently was because I weaned Olive.
The problem with switching back and forth between kids is that if I put Olive down once, then she just tantrums harder for me the next day. She also goes down more easily for Mr. Bee.
We could switch kids again, but will that just lead to the kids preferring one of us even more? Also it gives us a lot more flexibility when Mr. Bee can put Olive down for naps/bedtime instead of just me.
So the question is, how much do you try to counter parental preference?