Both sides have gotten kind of far out in the hype on this, Conservatives have pretty drastically overstated how much of the funding goes for abortion, and Liberals have done their best to label the other side as crazed killers of women.
However, the problem with giving PP money but just telling them they can't use it for abortion is that money is fungible, like a commodity, which means PP can take non-federal money out of something donors pay for now and move it in to fill the financial hole in their abortion operations, and fill the hole it left elsewhere with federal grant money.