I don’t have that doubt at all, not even one bit. I can relate to caring without feeling.
To what extent would you care takes care of this question and many related questions in future. Because “to what extent” shows the contrast between caring of a feeling being and an actually free being. To explain, feeling beings risk their life to a massive degree in order to protect their child. That’s what parental care for feeling beings means.
In the event of someone trying to stab your child, will you risk sacrificing your life by throwing yourself on the assaulter to protect your child? A feeling being for sure does. Or won’t you risk your life, because that is the most sensible thing to do for your body?