End-to-end (E2E) spoken language understanding (SLU) is constrained by the cost of collecting speech-semantics pairs, especially when label domains change. Hence, we explore \textit{zero-shot} E2E SLU, which learns E2E SLU without speech-semantics pairs, instead using only speech-text and text-semantics pairs. Previous work achieved zero-shot by pseudolabeling all speech-text transcripts with a natural language understanding (NLU) model learned on text-semantics corpora. However, this method requires the domains of speech-text and text-semantics to match, which often mismatch due to separate collections. Furthermore, using the entire collected speech-text corpus from any domains leads to \textit{imbalance} and \textit{noise} issues. To address these, we propose \textit{cross-modal selective self-training} (CMSST). CMSST tackles imbalance by clustering in a joint space of the three modalities (speech, text, and semantics) and handles label noise with a selection network. We also introduce two benchmarks for zero-shot E2E SLU, covering matched and found speech (mismatched) settings. Experiments show that CMSST improves performance in both two settings, with significantly reduced sample sizes and training time. Our code and data are released in https://github.com/amazon-science/zero-shot-E2E-slu.