Does social psychology include study of human cultures? Bertrand Russell (1872-1970), not a professional psychologist or anthropologist but a smart thinker and philosopher, believed that jealousy was one of the main sources of the sexual ethics of his time. I'm much interested in this kind of analysis, relating cultures, customs, norms, and traditions to basic human drives and emotions and also to other factors (geographical, economical, etc.). For example, why is there hijab in islamic world? Was it originated as a result of jealousy of men at some period of time at a specific region?

I would like to know if professional social psychologists today deal with such questions at least partially, and how they differ with anthropologists or sociologists in this respect, if at all.
I can see where the confusion may lay as the disciplines are very similar but different in their own ways.
Social Psychology

is about understanding individual behavior in a social context (McLeod, 2007).

This field of psychology therefore looks at human behaviour as influenced by other people along with the social context in which this occurs.
McLeod also points out that:

Topics examined in social psychology include: the self concept, social cognition, attribution theory, social influence, group processes, prejudice and discrimination, interpersonal processes, aggression, attitudes and stereotypes.

Cultural aspects of psychology will affect interpersonal processes etc. but in depth analysis of culture in psychology is covered by cultural psychology, which informs several other fields within psychology, including social psychology, cultural-historical psychology, developmental psychology, and cognitive psychology.
How they differ with anthropologists or sociologists in this respect.
Anthropologists
scientifically study human behaviour and societies in the past and present. Social anthropology studies patterns of behaviour and cultural anthropology.
Whilst anthropologists will study the cultures, past and present, they don't analyze the psychology of, or within, cultural differences.

Early anthropology originated in Classical Greece and Persia, and studied and tried to understand observable cultural diversity. As such, anthropology has been central in the development of several new (late 20th century) interdisciplinary fields such as cognitive science (Wikipedia).

Sociology
is the study of society, patterns of social relationships, social interaction and culture of everyday life. It is a social science that uses various methods of empirical investigation and critical analysis to develop a body of knowledge about social order, acceptance, and change or social evolution (Wikipedia). Sociology is also defined as the general science of society.
While culture forms part of society, again sociology doesn't deeply examine cultural aspects in the same way as anthropology or cultural psychology.
To understand more about the differences, please read the Wikipedia articles linked and follow the citations referenced in them.
References
McLeod, S. (2007). Social Psychology. Simply Psychology [Online].Retrieved from: https://www.simplypsychology.org/social-psychology.html