Cross-domain sequential recommenders (CSRs) are gaining considerable research attention as they can capture user sequential preference by leveraging side information from multiple domains. However, these works typically follow an ideal setup, i.e., different domains obey similar data distribution, which ignores the bias brought by asymmetric interaction densities (a.k.a. the inter-domain density bias). Besides, the frequently adopted mechanism (e.g., the self-attention network) in sequence encoder only focuses on the interactions within a local view, which overlooks the global correlations between different training batches. To this end, we propose an External Attention-enhanced Graph Contrastive Learning framework, namely EA-GCL. Specifically, to remove the impact of the inter-domain density bias, an auxiliary Self-Supervised Learning (SSL) task is attached to the traditional graph encoder under a multi-task learning manner. To robustly capture users' behavioral patterns, we develop an external attention-based sequence encoder that contains an MLP-based memory-sharing structure. Unlike the self-attention mechanism, such a structure can effectively alleviate the bias interference from the batch-based training scheme. Extensive experiments on two real-world datasets demonstrate that EA-GCL outperforms several state-of-the-art baselines on CSR tasks. The source codes and relevant datasets are available at https://github.com/HoupingY/EA-GCL.