If they aren't engaging in some full "Perseverance of the Saints" doctrine, they will still try to insist believing in Eternal Security is itself a motivation to do good out of appreciation. Even suggesting the Christians who do fall into Sin probably aren't believing in Eternal Security. But we should not bet on that.
The accusation of this post's title is not a valid criticism at all, it is irrelevant to if Eternal Security is true. The purpose of The Gospel is not to inspire good behavior, it's to inform people of what Jesus did. It's the religions of men that want to use the threat of eternal hell-fire or annihilation to keep people in line.
What should be our chief incentive to try and be faithful obedient Christians is that it will help spread The Gospel and get people Saved. The great commission says in the Greek to "Be a Witness". Evangelism isn't all about door to door soul winning and street preaching. Only certain people are called to be full time Evangelists. Hebrews 11 and James Epistle is about us justifying our faith to others. Being credible witnesses so people will consider our beliefs credible. Yet today it's popular to insist that you're NOT a good Christian if non believers don't hate your guts.
Let me give Biblical Proof to fellow Eternal Security believers that yes, some who are right on Eternal Security will take the Licence to Sin attitude even though they shouldn't. And that we therefor should not waste time trying to prove to our critics that none will.
I know it's popular to try and make Laodicea in Revelation 3:14-22 characteristic of Liberal Christianity. But reading the account without bias I have no doubt that one thing this Church does get right is Eternal Security. Doctrine is not exactly why they are doing so bad.
What I would say to those who'd use the message to Laodicea against Eternal Security is that their problem isn't being secure in their Salvation, but being Secure in their Reward. While Paul made clear in 1 Corinthians 3 some of the Saved will have no rewards.
Because thou sayest, I am rich, and increased with goods, and have need of nothing; and knowest not that thou art wretched, and miserable, and poor, and blind, and naked: I counsel thee to buy of me gold tried in the fire, that thou mayest be rich; and white raiment, that thou mayest be clothed, and that the shame of thy nakedness do not appear; and anoint thine eyes with eyesalve, that thou mayest see.When Jesus speaks of spitting them out of his Mouth it's not Hell but the Outer Darkness.
As I've said before I do believe there are ramifications when a Believer Sins. That is our second incentive.
Some who are right on Eternal Security even without the fifth point of Calivnism error, and acknowledging believers can sin. Want to limit those ramifications to only this world. Who take offense to the obvious fact that not all of the Saved are in New Jerusalem.
That is an error, and one that has allowed some Christians to become very hateful.