From looking at past campaigns, we know that this isn’t a systematic issue for all polling on Republican candidates ― in 2012, for instance, polling overestimated support for Mitt Romney. If support for Trump was uniquely stigmatized, you’d expect him to outperform his polls more than other Republican candidates did theirs. An analysis of 24 live-caller surveys in the AAPOR report, however, found Trump outperformed his estimates by an average 1.4 percentage points in 2016, compared with a virtually identical 1.3 points for GOP Senate candidates
Under the shy Trump voter theory, you’d also expect to see a pattern in how Trump’s numbers were affected by the mode in which a poll was conducted. Specifically, his support should have been consistently lower in polls that used live interviewers (in which Trump voters would need to admit their support out loud to another person) and higher in those conducted online or using automated phone calls (in which Trump voters merely had to click a button). This, however, didn’t happen. Nor was there any evidence of a relationship in the polls between support for Trump and the rates of voters saying they were undecided or were refusing to answer.
Voters might also have been less inclined to divulge their support for Trump to female or non-white interviewers than to white male ones. There was no evidence for this, either. As the report notes, none of this is conclusive evidence against the shy Trump voter hypothesis, but it is “inconsistent with expectations” of the theory.