How is it now that sin and the lifestyle has become the other of the day among Christians, even while we claim to have grace and live in the dispensation which covers our sins?

Yes it is true we live in the dispensation of grace and all our sins had been paid for and covered by Christ Jesus, but continuing in sin because of the dispensation we are in is total misconstrueing of grace.

Grace rather is the empowerment to live the supernatural life which is above sin, we don't continue to sin because we have grace, but rather we have grace which gives us the enablement not to continue in sin. Sin is supposed to be frowned at and rebuked by us all in this dispensation, even as the early Christians stood and spoke against it with great tenacity.

Them that sin rebuke before all, that others also may fear.

1 Timothy 5:20

Stay blessed and remain rapturable