To hear confession and give absolution.

The sacrament of confession in Catholic usage was called "shriving". To shrive is to give absolution in confession. Romeo tells the nurse that when Juliet comes to confession she will be "shrived and married". "Shrift" is the act of shriving in the same way that "theft" is the act of theiving, "belief" is the act of believing, and "thrift" was once the act of thriving, or "drift" the act of driving. ("I get your drift" still means the same as "I get what you are driving at")

Hamlet then substituted a forged letter ordering the English authorities to put Rosencrantz and Guildenstern to death, "no shriving time allowed".

To be killed "no shriving time allowed.", which means without the chance to confess and be forgiven for their sins. In other words, they get the same treatment as Hamlet Sr.

"They made love to this employment." Hamlet says that R & G chose to be spies, so he is not responsible if they meet a spy's death. It's a bit of sophistry, really, since even were that true, Hamlet didn't have to add "no shriving time allowed" so their souls would have to go to Purgatory rather than Heaven.