This is how I imagine a legalist sees someone who comes to Christ with a revelation of His grace, or for that matter just a person who holds to the Gospel of Grace. The idea that our sins are taken care of past, present, and future makes them think we can go out and sin all we want. The assumption is that grace gives us a license to sin. Don't worry though, the same question arose when the actual Gospel was preached by the apostle Paul.
Romans 6 King James Version (KJV)
6 What shall we say then? Shall we continue in sin, that grace may abound?
2 God forbid. How shall we, that are dead to sin, live any longer therein?
You see, this question can only arise when the proper gospel is preached. A gospel full of grace, full of Jesus and His sacrifice on the cross. This question cannot however be raised to those who would preach a message of mixture, or combining both Law and grace. If a preacher/evangelist were to say to a congregation that we must keep the Law, repent daily, and if we sin we must confess our sin in order to be forgiven, and we must live a holy and righteous life; do you suppose that this question could be raised? Of course not! The preacher would face palm, what he said went in one ear and out the other. He just preached a message of daily repentance from sin and this person asks if he can sin all he wants? It wouldn't make sense.
So, in what context can this question be raised? It can only be raised if indeed Christ's sacrifice took away ALL sin (past, present, and future) as the Word clearly reveals. He paid the price for sin, period. Such a question points to a Gospel that showers us in grace. To ask if we can sin all we want, points to the fact that we are forgiven completely. So the question comes up as, "Why then can't I sin all I want so that grace may abound?" The fact of the matter is, sin is taken care of (at the cross). All sin. The question implies that the messenger made it, ever, so clear that we are completely and totally forgiven.
It made me laugh when I saw that GIF and made me think of people who view the Gospel of Grace as a license to sin. That is how they imagine radical grace, but do not see that grace doesnt feed the flesh but speaks to the spirit. It is grace, not law, that makes sin have no dominion over us. It is grace that teaches us to deny ungodliness and worldly lusts. If you continue reading all of Romans 6 it continues to explain why we don't go on sinning, and it can be summed up as, "It no longer is who you are." You are dead to sin, and alive unto God. It isn't a license, but it sure does give liberty!