First, a remark which I think important (apologies, I'm donning my metrologist's hat). Nowadays, the units of the Imperial system or those of the CGS are all defined in terms of the SI units. For instance, 1 inch equals 2.54 centimetre by definition, and the centimetre in that definition is really the SI centimetre. This means that even in fields where non-SI units are traditionally employed, a basic knowledge of the SI is at least needed if one has to discuss units-related stuff.
I imagine that industry (e.g. Engineering) is still stuck using imperial units
Yes, you can still find pressures measured in pound-force per square inch (psi) or inch of mercury (inHg), areas measured in circular mil, heat measured in British thermal unit (BTU), wrench sizes measured in fractions of inch, etc. Product data sheets sometimes list parameters both in Imperial and SI units, sometimes no.
but research and physics are much better suited to SI units
Yes, Imperial units are definitely ill-suited for science. As for the dichotomy SI/CGS that has been brought up in the comments... uh, well, opinions might differ across disciplines, and if you skim through publications (journals, books) of different disciplines you will find different level of adherence to the SI (e.g. there are recent physics books which use the SI when discussing mechanics and the CGS when discussing electromagnetism).
How much of the teaching content at universities in the US is delivered in imperial units instead of SI?
I cannot answer this question directly because my contacts with the US are within my discipline and mainly outside of academia. However, I can try to answer it in an indirect way from the (limited) perspective of a compulsive book-buyer (that's me), assuming that the teaching content of lectures is roughly the same of books.
If I look at the books in my library, all the engineering books on electronics and electromagnetics written by US authors, even those from the 1960s, employ the SI. I could find only one exception, a book on lens design from the 1970s which employs Imperial units. None of the physics books employ Imperial units. Instead, the few mechanical engineering books that I have employ Imperial units, but they are very old.
Therefore, my impression, as reader of technical and scientific books from the other side of the ocean, is that nowadays most of the teaching content in the US is delivered in SI units, and that Imperial units are really limited to a few fields.