What issues, beliefs, backgrounds, and economic realities divided Americans in the 1980s, and how do these divisions shape the culture and politics of contemporary America?

The Eighties were also the decade in which the Religious Right had more power in American politics than it had wielded in decades.
During the 1970s, a small group of evangelical ministers, particularly Jerry Falwell, promoted the message that the gains of the late-1960 and early-1970s were incompatible with "family values," that is, the traditional family headed by a male who is married to a woman whose priority is to remain at home and care for their children. Falwell and company sought to scale back reproductive rights, particularly the nationwide constitutional right to an abortion, as decided in Roe v. Wade in 1973, as well as feminist gains in education, employment, political action, and personal finance.
Evangelicals capitalized off of discontent among white men, who worried that gains among women and minorities would rob them of privileges they had long enjoyed, in addition to making their social roles less clear. The religious right also exploited the ambivalences of people who thought that change was occurring to rapidly and wanted a safe return to the conventions of earlier eras. This partly explains why the Equal Rights Amendment (ERA) did not become a part of the Constitution in 1979. The religious right, working in concert with anti-feminist activists, most notably, Phyllis Schafly, convinced enough voters and representatives that the amendment would make it seem wrong for women to be homemakers and would lead to the expectation that women perform the same forms of labor and military service that were expected of men.
Similar messages are heard today from conservative politicians, religious political action committees (PACs), such as Focus on the Family, and from anti-abortion PACs, particularly the Susan B. Anthony Foundation.

Many different issues divided America in the 1980s, leading to many of the political issues still under debate.
One of the most important issues was race and how to remedy the long-lasting effects of slavery and other racial inequalities. Many of the solutions, such as desegregation and affirmative action, have proven of limited effectiveness and led to substantial backlash. An economic crisis in Mexico in the 1980s contributed to an increase in immigration, leading to issues which are still debated when discussing current immigration policy. Another important issue was the ongoing transformation of gender roles and realization of gender equality. 
On an economic front, this was a period of recession followed by a period of prosperity. However, it was a time during which inequality increased and prosperity gradually migrated from labor to capital. The wealthiest, who owned stocks or other forms of capital, got far richer than workers, and executive pay continued to outstrip worker pay. These problems of economic inequality persist today.