It is hard to define one culture for the entire Stellar Imperium except "cosmopolitan." This is more pronounced in the core sectors, where anything goes that doesn't step on the toes of the planetary government. The planetary governments are fairly lenient on cultural issues with two exceptions: alien bias and attacks on the Imperium. The Imperium frowns harshly upon any xenophobia, and anti-alien crimes and propaganda are dealt with harshly. However, this only applies to races that are part of the Imperium; aliens outside of the Imperium are considered "dangerous and anarchist," and are fair game. This goes as well for attacks on the Imperium: any governmental system other than the Imperium is considered "anarchist," and must be destroyed, while the Imperium is the only "secure" government. The Imperium licenses all interplanetary media, and any deviations from these party lines is grounds for revocation of license. While the individual planetary governors often wink at underground publications, interplanetary pirate media are hunted down ruthlessly.
Most media is delivered via home computer systems, with holographic feeds and dreamgames available on more advanced home systems. Dreamgame programming has replaced movie and game production as the most popular entertainment form, and most core planets support at least one dreamgame studio. However, dreamgame addiction is also a major problem on core planets, but the state welfare system provides enough income for even an addict to live comfortably.
Sporting events remain great attractions, even in an era of dreamgames. Regional and planetary championships are common, and some sports even have sector champions. With the advanced medical technology available, very few athletes have their careers ended by injuries, so sports are rather violent. However, blood is not the main goal. Variants of ancient football and basketball are common, with a variety of other sports rising and falling throughout the Imperium. Gambling is legal, so sports books are common. A new sport that has attracted a major audience is force-sword dueling, using special suits and swords that mimic damage without real risk to life and limb.
Society is heavily stratified in most cases; wealth buys a lot of things in the future. While most citizens are content, the wealthy can afford to be more than that. However, there are ways to move across social strata. The first is the Stellar Guard. Officers are paid very well, and even sergeants make more than the base civilian wage. A long-service Guard trooper can build up enough wealth to do well in the civilian world after retirement, with officers commonly moving into the Imperial Civil Service at good levels. The other method is the Planetary University. Each planet maintains a high-level university, with students selected by competitive examination given by the planet's education/culture AI. Social position doesn't count in this exam; only knowledge and cognitive skill matter. As such, intelligent members of the lower classes are often admitted. Once an applicant is admitted, there is no monetary charge; all books and other needs are provided by the university. However, upon graduation, the student is obligated to the Imperium for a period of fifteen years. While this may seem like a lot, remember that average ages are up to 150 years by this time, so fifteen years isn't as large an investment as it used to be. University-trained students are the top researchers and administrators in the Imperium, and are paid very well. Many actually continue in their Imperial positions after graduation, while others move into the private sector and become top managers.