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I have accepted a summer internship at a tax intern at an accounting firm of about 5000 employees. The position is in the state and local tax group. It is not a "legal internship" but does involve a lot of research on the tax code. I am excited about it, but I am wondering if this experience will hurt my chances of landing a proper "Attorney" job after graduation. I have experience working at two law firms as a legal intern prior to this.

No, it won't. Good experience to have on your resume, especially if your goal is to be a tax attorney.