On the staff side, the UI matters because the more "pleasant" a user interface is, the more likely staff is to actually use the system. (I define "pleasant" as easy to navigate, with very little screen noise; the data I need is right where I need it to be.)
On the customer side, UI matters because the more difficult the interface is, the less likely the customer is to use it, which means lower sales, lower engagement, and increased workload on staff.
The good news is, with more modern systems, you have more control over both of these UIs. On the staff side, your system should allow staff to rearrange data into a manner that is most fitting for their needs. On the customer side, your system should allow you to arrange the "flow" as you need it (e.g., membership joins, event registrations).
So take a look at the systems you have in place now. Do they allow staff to arrange their screens as they need them? Do they allow you to adjust how your customers experience joining, renewing, or registering for an event? Because they should.