If the level of the soil on the other side of the foundation perimeter walls is significantly higher than inside, and if the soil has a high moisture content, then this introduction of warm dry air into the crawl space might be necessary to keep it dry. I would definitely NOT shut off the air completely and if you reduce it to less than 1/3 of the current amount you should monitor the humidity and temperature in the crawl space.
It seems to me that the main problem with having significant air flow into the basement from the air handler is that the intake for the air handler is in the living space and so this amounts to a significant net pumping of air out of the living space. This would be especially the case if there is significant installed vent area to the outside from the crawl space. If there are no purpose built vents to the outside, then air pumped into the crawl space will cause exfiltration to the outside and back into the living space (the latter of which would be desirable, except for contaminants, if any).
So you could try to reduce to a minimum the airflow into the crawl space from the main air handler. Heat flow into the crawl space through the un-insulated floor of the heated living space above might keep the pipes from freezing. PEX is not destroyed by freezing but obviously it is not acceptable to allow it to freeze, especially since the couplings could be damaged by freezing. Insulating the PEX and the ABS drains could be done, but is not normally done and would interfere with detecting leaks.