To my knowledge, the people who are allowed to see your admissions records are the ones who decide whether or not you should be admitted. This may be: the department chair, the admission faculty of the department, the admissions office at the university, and the people who handle transcripts.

The only people who can see them, in essence, are the ones who deal with admission.
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The University’s privacy policy should address this. Every one of them is different.

You should also be aware that the duty of the professor is to teach, and knowing your background is important to that.
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The only stuff I can see are test scores (ACT and SAT), home address, placement scores, and college records. I get copies of my advisees’ HS transcripts. We don’t get to see any of the "extra" stuff like essays or letter’s of rec. Nor would we want to. Those things really have very little to do with how well you will do in our courses.
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I’m a college prof.