One way to accomplish what you are looking for would be to create two text boxes with the dates you want in red text. Then you can overlay them on top of those two dates on the x-axis.
If the dates that you would like to format might change somewhat frequently, I would recommend exploring Tableau's highlight action feature to dynamically select which dates you would like to highlight.
Your solutions helped me alot
No problem Jenny. Sometimes there isn't an 'out of the box' way to accomplish specific requests, but there is usually always a creative workaround that the user wouldn't even be able to tell the difference between.
If my answer solved your problem can you mark it as such?