Are cultural meanings stable and unchanging? Why or why not? Provide examples.

It seems that there is a constant struggle over cultural meanings, wherein there is an attempt to change and modernize them. There is resistance to the changing social mores and ideas by certain groups. Cultural meanings are definitely unstable, because throughout history they have changed drastically.
For instance, historical masculine and feminine roles were drastically different than they are today. Men, who would work in the fields and hunt, also tended to cook food for the family, while the women would tend to animals and work on the tools that were used in agriculture. The historical period tends to dictate the social and cultural norms. In that regard, cultural meanings are definitely not stable, although many people attempt to impose stability by forcing antiquated meanings on societal customs and norms.

"Cultural meanings" are stable or unstable depending upon the technological and social evolution of the individual society being examined. In other words, cultural meanings remain constant in certain societies—such as Aboriginal societies, which remain largely unexposed to modern life—but evolve continuously in liberal democratic societies where perceptions change over time. As an example, look to the evolving views on gender roles and increasing tolerance towards categories of individual previously subjected to discriminatory policies or practices. The latter category could include perceptions of homosexuality in any given culture. In western, liberal cultures, homosexuals have been looked down upon and discriminated against throughout history. In the 21st century, such discriminatory or prejudicial practices are less tolerated. In the United States today, LGTBQ communities enjoy considerably greater acceptance than they did only a short time ago. Contrast that with recent articles describing the operation of concentration camps in Chechnya, an Islamic republic in southern Russia, in which homosexuals or those suspected of homosexuality are being detained, tortured, and even killed. Long-established cultural beliefs about homosexuality in that isolated, war-torn region have obviously not evolved much over the centuries.
As noted, cultural meanings in long-established communities that are insulated from outside influences—such as those in remote, largely inaccessible regions—have often not evolved much, whereas we see cultural meanings in modern, technologically-advanced societies evolving much faster.