By "database" do you mean "table"? Are these two tables in the same file?
A quick fix is to define two relationships between projects and customers so that each set of fields uses a different relationship to look up the data.
In Manage | Database | Relationships, select the customers table occurrence (the box with this name) and click the duplicate button (Two green plus signs.)
That enables you to set up these relationships
Projects::CustomerID1 = Customers::CustomerID
Projects::CustomerID2 = Customers 2:::CustomerID
and now your second set of fields can look up from customers 2 instead of customers.
The long term fix may be to ask yourself if two customers will always be the most that can link to a project. What if you get a project where there are three or more customers? You wouldn't want a design that has to be modified in cases where the number of customers linked to a project increases.
If this is even a remote possibility, using a "join" table to link customers and projects so that you have a true many to many relationship here will be the better option as it enables you to link any number of customers to any number of projects.