COVID-19 has created a dramatic paradigm shift in education methods, which forced schools and universities to abandon the usual in-person education in favor of online education modules. Such a shift has extended the time and use of internet communication technologies (ICTs) by most, making online education platforms primary cyberattack targets. In this context, this study aims to explore parents, educators, and other caregivers' concerns about online education and the cybersecurity of their children and students. Thus, we conducted a survey-based study with 983 participants recruited through popular crowdsourcing platforms: MTurk and Prolific. Our results indicate a lack of technical support following cyber safety that the students received with the sudden transition to online education. Over 31% of our participants claimed that they never or rarely receive any communication related to cyber safety from the students' educational institutions. Additionally, our analysis shows that the student support structure needs to be trained and informed on the threats faced by children online and on the ways to mitigate these threats. Finally, we find a statistically significant difference between parents, educators, and other caregivers regarding their perceptions of children's online privacy and cyber safety. We conclude this work by providing actionable recommendations to promote privacy-preserving and digitally secure online education.