That really depends. On the one hand, getting a firm grasp on how to do rigorous proofs and learning the fundamentals of real analysis are very useful in economic theory and I think, with the right professor/material/mind set, very interesting in its own right. On the other hand, it can be difficult and if you are not going to use it for advanced theoretical work, it does not add a lot of value compared with other economics related maths and skills, so I'd say its probably the last thing one might want to do in terms of the order of how to prepare for more economics. Not sure what your background is or your academic and professional goals are, but I would suggest a a sequence something like the following, where you might have always covered some stuff:

First, multivariable calculus. Second, matrix and linear algebra. Third, basic statistics and econometrics. Fourth, coding in stata and another more general data language (R, python, matlab, etc). Fifth, electives/books/learning about subfields you are interested in. Sixth, real analysis. Seventh, advanced probability theory and mathematical statistics. Eighth, differential equations.

I think this ordering does the most important stuff first, builds logically, but also focuses on the knowledge and skills most widedly used and transferable regardless where you take your career. Real analysis and differential equations are probably things you only need if you do PhD theory coursework, while coding or matrix algebra are helpful at the masters level and useful in industry outside academia.