Is liquid fabric softener bad for the washer? (Or dryer?)

It’s fine. Just don’t put it in until the washer is full of water. It can cause “oil spots” on clothes if put in before.

Google has several entries referring to but not necessarily answering, Is liquid fabric softener bad for your washer?

I gave the page a brief perusal, but so far I haven’t seen anything attributed to the infallible wisdom of SOG. ;-o

Don’t put it in the dryer!

Softeners will cause long term discoloration of your clothes as the chemicals coat the material and turn yellow.

I don’t use anything except detergent and sometimes bleach.