Our paper tackles the topic of the digital technologies (represented by the information and communication technologies (ICT)) and the sustainable transformation and energy safety in households represented by the smart homes and the traditional households using smart appliances, gadgets, as well as smart meters connected to the Internet. The rapid growth and adoption of information and communication technologies, such as computers, mobile devices, sensors, and networks, can seriously affect the ways and amounts of energy used by society on its path toward sustainable development. There is a growing interest in characterizing the net energy impact of ICT as well as the Internet of Things (IoT) that arises from indirect effects that offset (or amplify) the energy directly consumed by ICT equipment. However, the society might need some time to build the trust in these new digital technologies and develop the wide social acceptance for their usage. In order to test these assumptions, we employ an empirical econometric model based on the data obtained from the online survey carried out with the randomly selected respondents (N = 523) from Russian Federation and the four European Union (EU) countries (Czech Republic, Germany, Poland, and Slovakia). Even with regard to the small size of the sample and thence the limitations stemming from that fact, our results demonstrate that familiarity with smart home technologies and the possibility to alter the tariffs and use flexible energy demand increase the safety of residents and consumers. In addition, it appears that energy efficiency is being rewarded, as energy consumption is sensitive to time constraints on supply. Furthermore, we find that respondents’ age (43% of the respondents belonged to the 36–55 age group), positive attitude to smart home technologies and the possibility to exploit the flexibility of demand offered by the variety of energy tariffs during and off-peaks all yield quite strong and positive relationships and correlations with the willingness to accept the smart home technology and the flexibility of demand. At the same time, concerns over personal security or sharing personal data related to energy consumption do not constitute major concerns for the respondents. Our results have some important impacts on the overall strategy for pursuing sustainable economic development and following the Sustainable Development Goals (SDGs) that might be useful for stakeholders and policymakers as well as for the researchers in this field.