Carriers often enter new shipping markets and undertake corporate social responsibility (CSR) activities to attract more shippers. CSR generally refers to the integration of social and environmental factors by a firm into its business decision-making. This paper constructs a shipping supply chain composed of one port, one carrier, and one potential entrant carrier, where both carriers are committed to CSR activities. Two possible channel structures of the incumbent supply chain are considered: centralization and decentralization. Under both structure settings, we study the entry strategy of the entrant, accommodation strategy of the port, and impacts of entry on consumer surplus and social welfare. Our results show that (i) the entry and accommodation strategies depend on the CSR levels of carriers; (ii) downstream entry improves social welfare under centralization but may decrease it under decentralization; (iii) the entrant has more incentive to enter under decentralization than under centralization when the incumbent carrier has a high CSR level. However, the port might have less incentive to accommodate entry under decentralization; (iv) channel decentralization may improve consumer surplus and social welfare when the port accommodates the entry, while hurts these when the port deters the entry. Additionally, we find that under the case of endogenous CSR level, the entry and accommodation strategies depend on the CSR investment cost coefficient; and the entrant has a stronger entering incentive under uniform pricing than under differentiated pricing if the incumbent carrier has a low CSR level.