It really depends on how you're trying to visualize this specifically.
You could create a calculated field to 'convert' your text status into a number i.e. IF [Status] = 'Open' then 1 elseif [Status] = 'Closed' then 2 END. You could then use this as a measure, set the aggregation to MIN and color it that way. You could use your text based equivalent as a label.
But it sounds to me like you're going to want to put this alongside other actual measures - fields / metrics that are actually measuring things.
So it's sort of hard to provide guidance without knowing specifically what layout you're trying to get to and the structure of your data. Please upload a Tableau Packaged Workbook with some sample data along with some more details on how you're trying to visualize this and we'll go from there.
On my Y axis I was looking to have the project status and the name of the projects listed on the X axis. The number of projects on the x axis was limited to 10, as the manager only wanted to see the top 10 projects. I was then wanting to plot the status against each project and colour code that plot. I was thinking of using the circle view graph and instead of colouring the circles by project I wanted to colour them by the status. On the Y axis I want the name of the Status rather than a number
I have attached a spreadsheet with basic sample data. The spreadsheet contains 2 worksheets: Project Status Name and Project Status Number. In my source data the status field (and similar fields) are all text fields. I added the number worksheet just to start playing around and have also attached the tableau result