In Bayesian data analysis, parameters are treated as random variables. This stems from the Bayesian subjective conceptualization of probability. But do Bayesians theoretically acknowledge that there is one true fixed parameter value out in the 'real world?'

It seems like the obvious answer is 'yes', because then trying to estimate the parameter would almost be nonsensical. An academic citation for this answer would be greatly appreciated.

IMHO "yes"! Here is one of my favorite quotes by Greenland (2006: 767):


  It is often said (incorrectly) that ‘parameters are treated as fixed
  by the frequentist but as random by the Bayesian’. For frequentists
  and Bayesians alike, the value of a parameter may have been fixed from
  the start or may have been generated from a physically random
  mechanism. In either case, both suppose it has taken on some fixed
  value that we would like to know. The Bayesian uses formal probability
  models to express personal uncertainty about that value. The
  ‘randomness’ in these models represents personal uncertainty about the
  parameter’s value; it is not a property of the parameter (although we
  should hope it accurately reflects properties of the mechanisms that
  produced the parameter).


Greenland, S. (2006). Bayesian perspectives for epidemiological research: I. Foundations and basic methods. International Journal of Epidemiology, 35(3), 765–774.
