2 Thessalonians 1:4-5
4 So that we ourselves glory in you in the churches of God for your patience and faith in all your persecutions and tribulations that ye endure:
5 Which is a manifest token of the righteous judgment of God, that ye may be counted worthy of the kingdom of God, for which ye also suffer:
Does the above passage teach that unless we endure "persecutions and tribulations" for our faith, we will not be "counted worthy" for entrance into Heaven, and will instead be summarily cast into Hell?
What is in view here is kingdom inheritance, not kingdom entrance.
Entrance is predicated on having the New Birth (John 3:3-5), which is obtained at the moment of faith in Jesus Christ (1 John 5:1, Galatians 3:26, John 1:12). Nothing can ever jeopardize that New Birth once it occurs, because it is born of "incorruptible seed" (1 Peter 1:23), and this "seed remains in him" (1 John 3:9), and so he "cannot sin" (1 John 3:9, 5:18). The doctrine of the New Birth is covered in much more detail in this article.
Inheriting the kingdom, however, in contrast to the gift of Eternal Life (Romans 6:23) that gets us into the kingdom in the first place, is a reward for those who serve the Lord, which includes, as the verse in question states, enduring persecution and tribulation for one's faith:
Colossians 3:23-24
23 And whatsoever ye do, do it heartily, as to the Lord, and not unto men;
24 Knowing that of the Lord ye shall receive the reward of the inheritance: for ye serve the Lord Christ.
2 Timothy 2:12-13
12 If we suffer, we shall also reign with him: if we deny him, he also will deny us:
13 If we believe not, yet he abideth faithful: he cannot deny himself.
Above, we are told we will receive the reward of the inheritance, predicated on service, and we will reign with Him, if we suffer here in this life for Him. This is certainly not describing a "free gift" (Romans 5:15-18), because kingdom inheritance is distinct from kingdom entrance.
This distinction is covered more in this article on some other verses which mention "inheriting" the kingdom (1 Corinthians 6:9-11, Ephesians 5:5-6, Galatians 5:19-21), as well as this one, which deals with the doctrine of rewards in Scripture more generally, if you'd like some further reading on the topic.
Do we merit entrance into the Kingdom of God by suffering for Him? Absolutely not. God does, however, give us the opportunity to increase our inheritance in the kingdom, based on what we do here in this life. This is a major teaching in the New Testament, and the passage in question from 2 Thessalonians presents no problem whatsoever for the Free Grace understanding of rewards in distinction from Salvation.