Anything by John Osborne would fit the description of intergenerational conflict plays as he was a member of the so-called Angry Young Man movement, and sociopolitical. Not very contemporary though.

One that comes to mind is Fences by August Wilson. It depends a little bit what you mean by "political," but this play definitely deals with racial politics in the US and intergenerational conflict. Another one that also deals with racial politics but with an undercurrent of intergenerational conflict is A Raisin in the Sun by Lorraine Hansberry. Lillian Hellman's The Little Foxes deals with gender politics in the US and has themes of conflict between the generations. Clifford Odets' Awake and Sing! addresses class conflict and generational conflict. None of these plays deals directly with politics in the narrow sense of electoral politics, political institutions, political office holders, and so on. But they all address significant social issues that are political in the broader sense of power relationships.

Howdy Layla! My first thought is The Crucible. Although it is ostensibly set during the Salem witch trials, Miller intended the work to function as a critique of the excesses of contemporary political “witch hunts”, specifically McCarthyism and HUAC. The primary antagonistic relationship in the play is between young accuser and adult interrogator/investigator.