This crisis will impact so much of our lives--it's difficult to even imagine a part of how we live that won't be turned upside down--from how we think about letting people into our personal space to what content we watch on TV.
As marketers it will also impact every part of how we market as well, regardless if our product, customer, and marketplace is in the direct line of fire of the impacts of the virus or actually thriving in its wake.
From how we speak to customers to how we help them see and find value in our services and products, there will be a long road back. We'll have to consider the impacts on our customers personally; their budgets; how their teams have been impacted; what technology or service is at the top of their priorities; how they are reassessing their own business models--the list goes on and on.
What needs to remain constant, however, is that we put them at the center. Whether you call that being customer "obsessed" or customer "centricity" the object is still the same--never leave their side. Help them, be there as a resource, offer something of value, make a joke, send lunch, offer a promo--whatever you can do to help them ease back into the normal cycle of things, that's our job once this crisis passes.