Exploration of the impact of personality traits on social interactions within anonymous online communities poses a challenge at the interface of networked social sciences and psychology. We analyze whether Myers-Briggs Type Indicator (MBTI) personality types impact the dynamics of interactions on an anonymous chat system with over 288,000 messages from 6,076 users. Using a data set including 940 users voluntarily providing MBTI typing and gender, we create a weighted undirected network and apply network-science measures-such as assortativity, centrality measures, and community detection with the Louvain algorithm-to estimate the level of personality-based homophily and heterophily. Contrary to previous observations in structured social settings, our research shows a dominance of heterophilous interactions (89.3%), particularly among cognitively complementary types, i.e., NT (Intuitive-Thinking) and NF (Intuitive-Feeling). However, there is a moderate level of personality-based homophily (10.7%), notably among introverted intuitive personalities (e.g., INTJ, INFP, INFJ), reflecting an underlying cognitive alignment that persists regardless of identity markers. The interaction network exhibits scale-free properties with a power-law exponent of 1.45. In contrast, gender is a stronger homophily attribute, as evidenced by stronger levels of female users' group interactions compared with male users. While MBTI type influences minor interaction preferences, community structure exhibits low modularity (Q = 0.2584). The findings indicate that, in the absence of identity cues, psychological traits subtly shape online behavior, blending exploratory heterophily with subtle homophilic inclinations.