Vaccine hesitancy is considered as one of the leading causes for the resurgence of vaccine preventable diseases. A non-negligible minority of parents does not fully adhere to the recommended vaccination schedule, leading their children to be partially immunized and at higher risk of contracting vaccine preventable diseases. Here, we leverage more than one million comments of 201,986 users posted from March 2008 to April 2019 on the public online forum BabyCenter US to learn more about such parents. For 32% with geographic location, we find the number of mapped users for each US state resembling the census population distribution with good agreement. We employ Natural Language Processing to identify 6884 and 10,131 users expressing their intention of following the recommended and alternative vaccination schedule, respectively RSUs and ASUs. From the analysis of their activity on the forum we find that ASUs have distinctly different interests and previous experiences with vaccination than RSUs. In particular, ASUs are more likely to follow groups focused on alternative medicine, are two times more likely to have experienced adverse events following immunization, and to mention more serious adverse reactions such as seizure or developmental regression. Content analysis of comments shows that the resources most frequently shared by both groups point to governmental domains (.gov). Finally, network analysis shows that RSUs and ASUs communicate between each other (indicating the absence of echo chambers), however with the latter group being more endogamic and favoring interactions with other ASUs. While our findings are limited to the specific platform analyzed, our approach may provide additional insights for the development of campaigns targeting parents on digital platforms.