How to argue against questionable research practices such as P-hacking and Harking?
This sort of thing happens in both the social sciences AND physical sciences.  For instance, often a scientist will collect data to test a theory but will also collect lots of extraneous data.  Analyses on these extraneous data often should be considered exploratory and labeled as such (because significant results could be due to the multiple tests)  [As another example, you don't want to know how often chemists repeat an experiment until they get a good yield, then stop and report that yield without mentioning that that was the best in 20 experiments!]

The fastest solution is to agree to do the multiple analyses, but then tell what you did in the methodology section.  If you say that you analyzed it several ways and one way showed significance, readers can decide whether or not to believe the result.  Just tell your co-authors that not mentioning that you did multiple analyses is leaving the research improperly described.

However, you can (occasionally) save the day.  If, for instance, you did 10 different analyses and picked the best one, you'll be ok if the result would hold under a Bonferroni correction (i.e. instead of requiring significance at the 0.05 level, you require significance at the 0.05/#tests level).  So it the final test shows a p-value such as 0.000001, you probably are on safe grounds.

Another approach is to a priori decide that some tests are obvious (confirmatory) and some are just searching around the data (exploratory).  Then you can demonstrate the confirmatory results, while labeling anything interesting among the 'exploratory' results as 'needs further research'.  That is, you can mix well-founded tests with 'data dredging' as long as you acknowledge the difference between the two sets of tests.

But if it isn't possible to rescue the result, I'd go with insisting that they describe what they did, with the comment that if they are embarrassed to describe it, they shouldn't have done it.  :)

You might also add that it is often obvious (at least to statisticians) that a researcher has pulled this trick.  When we see a test in isolation that would not occur to us to be the obvious approach, or a hypothesis that we'd not choose a priori, it looks suspicious.  For instance, I recently read a paper that claimed that a certain group of people tend to commit suicide more often if they were BORN in the Spring.  It was clear that JUST testing the effect of birth in Springtime was not something that would occur to anyone, without testing the effect of birth in other seasons.  So they probably had a spurious result due to multiple comparisons.