Yes, gender-specific rules exist in plenty of destinations, and they usually show up in three areas: dress, access to spaces, and interaction norms. Dress codes affect women more visibly, from headscarf requirements at certain religious sites to expectations of covered shoulders and knees, but men are not exempt; shorts and sleeveless tops can bar men from temples, churches and mosques too.
Access rules include women-only train carriages in several countries, separate security lines at some airports, gender-segregated prayer halls, and bathhouses or spas that admit one gender at a time or on different days. Some religious sites restrict entry to one gender entirely for specific inner areas.
Interaction norms matter as much as written rules. In more conservative cultures, physical contact between unrelated men and women, even a handshake, may be declined; let the other person initiate. None of this is hard to navigate once you know it exists.