I do not believe that any is "beyond saving" for Jesus. The Bible also warns us to watch against wolves in sheep's clothing (Matthew 7:15), false teachers (2 Peter 2: 1-3), and those who would alter God's Word (Revelation 22:18-19).
Good. Neither do I.
The Holy Father apparently agrees with the two of us:
If a person is gay and seeks the Lord and has good will, who am I to judge him?