Is there an introduction to probability and statistics that balances frequentist and bayesian views?

I would recommend the following 16-page article from 36 years ago, which is easily accessible to any upper-level undergraduate:

"Controversies in the Foundations of Statistics", Bradley Efron, The American Mathematical Monthly, vol. 85, 1978, pp. 231-246.

This won an MAA Writing Award.

In my inexpert opinion, it is quite unsettling. It does not offer a resolution.

Edit: The above-mentioned article impressed me when I was a student. But there has been much follow-up. For example:

"A Two-Hundred-and-Fifty-Year Argument", Bradley Efron, LASR 2011 — Next Generation Statistics in Biosciences (Proceedings, 30th Leeds Annual Statistical Research Workshop), 2011

"Bayes Theorem in the Twenty First Century", Bradley Efron, Science 340, June 7, 2013

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Further edit: Oops, my ignorance is showing.

B. Efron was president of the ASA in 2004; see his presidential address "Bayesians, Frequentists, and Scientists" at https://www.asapresidentialpapers.info/documents/Efron_2004_BAK_01-05-10.pdf.

He recently won the Guy Medal in Gold, https://en.wikipedia.org/wiki/Guy_Medal.

See also http://statweb.stanford.edu/~ckirby/brad/EfronCV.pdf and https://en.wikipedia.org/wiki/Bradley_Efron and https://math.stackexchange.com/a/116444/18972.