I assume that you are asking us to apply Rawls' ideas to an issue in today's society. I have changed your question to reflect that.
One good issue to use to illustrate the veil of ignorance is the issue of gay marriage. To use Rawls' veil of ignorance, we must imagine that we would not know whether we ourselves are going to be gay or straight. We must then ask ourselves what sort of laws we would advocate with regard to gay marriage if we were unaware of this fact about ourselves. Presumably, if we did not know whether we were gay or straight, we would advocate laws that would permit gay marriage. We would want to be sure that we would be allowed to marry and to have committed relationships regardless of what our sexual orientation happened to be.
So, by using Rawls' veil of ignorance, we can see that (to him) laws allowing gay marriage would be more just than laws that ban it.