Those not well studied in God's Word probably aren't going to like this.
What Apostle Paul said in Acts 16:31 is true, believe on Jesus Christ and one will be saved. The question is though, the WHEN, literally, physically, and I mean being established in Christ's future Kingdom at His future coming.
Not all believers on Christ Jesus can sit upon the 12 thrones Lord Jesus promised only to His elect chosen Apostles (Matthew 19:27-30).
In the next Matthew 20 Chapter, Lord Jesus addressed this matter of rewards in His future Kingdom...
Matt 20:20-23
20 Then came to Him the mother of Zebedee's children with her sons, worshipping Him, and desiring a certain thing of Him.
21 And He said unto her, "What wilt thou?" She saith unto Him, "Grant that these my two sons may sit, the one on Thy right hand, and the other on the left, in Thy kingdom."
22 But Jesus answered and said, "Ye know not what ye ask. Are ye able to drink of the cup that I shall drink of, and to be baptized with the baptism that I am baptized with?" They say unto Him, "We are able."
23 And He saith unto them, "Ye shall drink indeed of My cup, and be baptized with the baptism that I am baptized with: but to sit on My right hand, and on My left, is not Mine to give, but it shall be given to them for whom it is prepared of My Father."
KJV
Per Ezekiel 44, only the ZADOK priests, which represent the faithful followers of Christ Jesus that remain in Him and His Word all the way to the end, only those will be allowed to approach Jesus in His future Millennium Kingdom and serve at His table. It shows the Levites who erred when Israel fell away, will still be in charge of the future Millennial temple duties, but they won't be allowed to approach Christ in that future time.
We indeed are saved only... by Faith on Jesus Christ, through God's Grace, unmerited favor we could never earn ourselves. However, our 'works' in Christ do follow us to Heaven, as written...
Rev 14:12-13
12 Here is the patience of the saints: here are they that keep the commandments of God, and the faith of Jesus.
13 And I heard a voice from heaven saying unto me, "Write, Blessed are the dead which die in the Lord from henceforth: Yea, saith the Spirit, that they may rest from their labours; and their works do follow them."
KJV
I do not recognize my 'works' in Christ Jesus as being anywhere near... many Christian brethren that have gone before me. I will feel lucky just barely... being saved by our Lord Jesus Christ to be in His future Kingdom. I know I am not worthy to sit upon a throne to reign with Him either, nor do I ask like those two sons of Zebedee whose mother wanted Jesus to promise they would sit upon Jesus' right hand and left hand in His future Kingdom. If Lord Jesus saves me from my sins remembering me in His future Kingdom, that will be good enough for me. I hope I will be counted faithful by Him when He comes, and will be able to serve Him at His table, or at the least be one of His priests, but like He told the mother of Zebedee's two sons, it is The Father's decision to decide who will do what in His future Kingdom.
Now my main point in this:
Remember the "unprofitable servant" in Jesus' Matthew 25 parable of the talents? That servant did nothing with what he was given, showing that he just believed and that's all. He buried the one talent he was given, and when his master returned, he gave that one talent back to him; didn't even bother to put the talent to work to draw interest. Jesus showed that servant will be cast to the "outer darkness" when Jesus returns. All the others Jesus gave talents to was according to their ability, and they each produced 100% fruit. But not that one given only the one talent.
We are to learn a lesson from this. Our works do follow us to Heaven, but we are not saved by our works. However, Lord Jesus showed lack of works in Him can... place a believer in His future Kingdom in a precarious spot, because that "outer darkness" represents a place of shame, in separation from Jesus when He comes. It does not mean that servant won't eventually be saved in Christ; but it does mean that one will stand in judgment throughout Christ's "thousand years" reign with His faithful elect. And how much worse will it be for those brethren that 'fall away' to the coming false-Messiah that appears first in Jerusalem, thinking he will be our Lord Jesus?
This is why Apostle Peter said the following...
1 Peter 4:16-19
16 Yet if any man suffer as a Christian, let him not be ashamed; but let him glorify God on this behalf.
17 For the time is come that judgment must begin at the house of God: and if it first begin at us, what shall the end be of them that obey not the gospel of God?
18 And if the righteous scarcely be saved, where shall the ungodly and the sinner appear?
19 Wherefore let them that suffer according to the will of God commit the keeping of their souls to Him in well doing, as unto a faithful Creator.
KJV