In Kruschke's book, in chapter 11, he gives an example of testing whether a coin is biased. He shows how, if one conditions on $N$ (the number of flips), $z$ (the number of heads), or on the duration ($N$ is then given a Poisson distribution), then we get different sampling distributions, and consequently, different decisions, confidence intervals, etc. The reason given for why it's OK in a classical frequentist context to do this type of conditioning is because,
... will result in exactly 5% false alarms in the long-run when the null hypothesis is true.
Why is it allowed? What's the 'math' behind this statement?
The Bayesian interpretation of data does not depend on the covert sampling and testing intentions of the data collector. ...The likelihood function captures everything we assume to influence data.
Hence, why can't we condition in a similar way the Bayesian analysis and check for different posterior distributions, while using the exact same priors? Why isn't the likelihood altered by different 'generating sample procedures', but the sampling distribution is?