Memory disaggregation is a promising technique in datacenters with the benefit of improving resource utilization, failure isolation, and elasticity. Distributed hashing indexes have been widely used in memory systems to provide fast lookup services. However, traditional distributed in-memory hashing indexes become inefficient in disaggregated memory since the compute power in the disaggregated memory pool is too weak to execute complex index requests. To provide efficient indexing services in disaggregated memory, this paper proposes RACE hashing, a one-sided RDMA-Conscious Extendible hashing index with lock-free remote concurrency control and efficient remote resizing. RACE hashing enables all index operations to be efficiently executed by using only one-sided RDMA verbs without involving any compute resource in the memory pool. To support remote concurrent access with high performance, RACE hashing leverages a lock-free remote concurrency control scheme to enable different clients to concurrently operate the same hashing index in the memory pool in a lock-free way. To resize the hash table with low overheads, RACE hashing leverages an extendible remote resizing scheme to reduce extra RDMA access caused by extendible resizing and allow concurrent request execution during resizing. Extensive experimental results demonstrate that RACE hashing outperforms state-of-the-art distributed in-memory hashing indexes by 1.4~13.7X in YCSB hybrid workloads.