In June 2024, X/Twitter changed likes' visibility from public to private, offering a rare, platform-level opportunity to study how the visibility of engagement signals affects users' behavior. Here, we investigate whether hiding liker identities increases the number of likes received by high-reputational-risk content, content for which public endorsement may carry high social or reputational costs due to its topic (e.g., politics) or the account context in which it appears (e.g., partisan accounts). To this end, we conduct two complementary studies: 1) a Difference-in-Differences analysis of engagement with 154,122 posts by 1068 accounts before and after the policy change. 2) a within-subject survey experiment with 203 X users on participants' self-reported willingness to like different kinds of content. We find no detectable platform-level increase in likes for high-reputational-risk content (Study 1). This finding is robust for both between-group comparison of high- versus low-reputational-risk accounts and within-group comparison across engagement types (i.e., likes vs. reposts). Additionally, while participants in the survey experiment report modest increases in willingness to like high-reputational-risk content under private versus public visibility, these increases do not lead to significant changes in the group-level average likelihood of liking posts (Study 2). Taken together, our results suggest that hiding likes produces a limited behavioral response at the platform level. This may be caused by a gap between user intention and behavior, or by engagement driven by a narrow set of high-usage or automated accounts.