Part of the reason why we have hope in Jesus is because of what we did. We've talked about how Jesus provided the "great exchange" via the cross and resurrection throughout Romans, but one particular note is that Jesus "died for the ungodly" -- even though "we were still without strength" (5:6).
As for the significance of dying for the ungodly, Paul notes that very rarely do people die on behalf of someone else (sacrificial love), and in almost all cases, it's for a good man (5:7). In other words, in most circumstances, people probably don't die for others that go against them. So with God's high standards and attention to detail on how we treat others, we don't even deserve receiving God's love -- but Jesus did it anyway.
In fact, God's great love is demonstrated "while we were still sinners" (5:8). Even for people who want to have nothing to do with God! Considering that Jesus didn't wait for us to change our behavior and beliefs when he died on the cross, Jesus demonstrated that loving others without agreeing with every single decision or viewpoint is actually possible. Because of what Jesus did, we can receive Jesus's gift of His righteousness, peace, and hope, and considering that we have the Holy Spirit, we can be empowered to show Christ-like love to others even without agreeing with every single decision or viewpoint.