Difference between 要学习的东西 and 东西要学习
People like variations in word order. The word order is not fixed forever. I don't think a proscriptive approach to grammar is helpful. In the end, natural language will win.

Like Marko commented, "as in the things need to study, which is obviously not the intended meaning of the sentence"

The basic sentence is:
我有东西。
【】is then an adjective.
我有【（我）要学习】的东西。
I have things I want to/must study

This below works because we know 东西 don't study, people study.

我有很多东西（我）要学习。
I have many things (that) I want to study.

Put a noun like 学生 in there that can study and the student is no longer 我:

我还有很多学生要学习（这门课程）。
I still have many students (who) want to study this course.