When parties decide, do voters listen? We argue that the answer depends on voters' trust in the institutions of American politics. Using both a conjoint experiment and a traditional survey experiment with subjects voting in hypothetical congressional primary elections, we find that respondents from both parties are more likely to support a candidate when that candidate is endorsed by a member of the party or when the candidate has previously served in elected office. However, these findings are conditional on trust and partisanship. For Democrats, we find that support for party-backed candidates erodes among low-trust respondents. Low-trust Democrats are particularly resistant to candidates endorsed by traditional party elites such as Speaker Pelosi, President Obama, and the Democratic Congressional Campaign Committee, and are less likely to support experienced candidates. While low-trust Republicans are more skeptical of endorsements from traditional party actors like Senate Majority Leader Mitch McConnell, the most salient attribute for Republicans is an endorsement from President Trump, which significantly boosted support in both studies independent of trust. Our findings support party-centric theories of primaries but suggest that voter distrust in the political system threatens parties' control over their nominations.