Can a private landowner legally charge for hunting/fishing access to their property?

Yes. A landowner can charge for fishing or hunting access to their property, but cannot charge you for game harvested from their property.
However, if a landowner has a permit to operate a commercial “put and take” fishing operation from their private impoundment, they may charge for fishing and/or a fee-per-fish or per pounds of fish.
If a landowner has a licensed game farm and a shooting preserve permit, they can charge you a fee to hunt game birds on their property. The fee may be charged for access or you may be charged for each bird released or harvested.