Can I share iCloud storage without also agreeing to pay for iTunes purchases?
No. Family sharing in spring 2018 and back to when it started implies one payment card for all purchases. 

The only exception of course is store credit or gift card balance can be applied to any or all parts of a family so that most purchases pull from that prepaid balance. So if you manage it or push out “allowances”, most of the time, only recurring payments and IAP hit the shared card.