User-generated item lists are popular on many platforms. Examples include video-based playlists on YouTube, image-based lists (or"boards") on Pinterest, book-based lists on Goodreads, and answer-based lists on question-answer forums like Zhihu. As users create these lists, a common challenge is in identifying what items to curate next. Some lists are organized around particular genres or topics, while others are seemingly incoherent, reflecting individual preferences for what items belong together. Furthermore, this heterogeneity in item consistency may vary from platform to platform, and from sub-community to sub-community. Hence, this paper proposes a generalizable approach for user-generated item list continuation. Complementary to methods that exploit specific content patterns (e.g., as in song-based playlists that rely on audio features), the proposed approach models the consistency of item lists based on human curation patterns, and so can be deployed across a wide range of varying item types (e.g., videos, images, books). A key contribution is in intelligently combining two preference models via a novel consistency-aware gating network - a general user preference model that captures a user's overall interests, and a current preference priority model that captures a user's current (as of the most recent item) interests. In this way, the proposed consistency-aware recommender can dynamically adapt as user preferences evolve. Evaluation over four datasets(of songs, books, and answers) confirms these observations and demonstrates the effectiveness of the proposed model versus state-of-the-art alternatives. Further, all code and data are available at https://github.com/heyunh2015/ListContinuation_WSDM2020.