I know that the Bible tells believers to seek for eternal rewards rather than earthly riches, but Psalm 128 (among other passages) tells us that God blesses us in the here and now. Is it wrong for a believer to desire both earthly and eternal blessings?
A believer may certainly petition God for blessings of any kind, but we should always remember God blesses us according to what He deems best. For example, Psalm 128 describes an earthly blessing of possessing a fear of the Lord, which is probably not the earthly blessing you were imagining, but this is typical of Scripture. We value things like wealth, fame, physical health and the like, so we call them "blessings," but the Lord knows that in the long run these things are more curse than blessing. Wealth leads to greed and dissipation, fame leads to pride and arrogance, and physical strength leads to lustful tendencies, etc.
Instead, the Lord may leave us in want for these things to encourage our dependence upon Him and to protect us from temptation. Only after we have the benefit of hindsight in Heaven will we likely understand how we benefited. Like children who want to eat candy instead of vegetables, we think we know what's best for us, but our Father in Heaven knows better. So while it's natural to desire earthly pleasures (which we call blessings), we should be prepared for the Lord to bless us in ways that further our spiritual growth and eternal rewards.
In Matthew 6 Jesus says that a person cannot serve two masters, God and wealth. Serving one means forsaking the other. Instead, So Jesus instructs us to seek God’s kingdom and His righteousness knowing the rest will be given to us in due time:
Considering this teaching, we then return to Psalm 128 to understand that the psalmist is describing a person who is not worried about what he will eat or drink or wear. Such a person trusts that the Lord will take care of such things. As such, he will be happy “when you shall eat of the fruit of your hands” (Psalm 128:2). Furthermore, with respect to his wife and children, it appears that they, too, are believers, as the text says, “How blessed is everyone who fears the LORD.”
So, our motivation for living Godly lives in Christ Jesus is to glorify God. As 1Corinthians 10:31 says:
And as Romans 12 says:
We do this by doing good (practicing His righteousness) and seeking His kingdom. This would include evangelizing the lost and making disciples. It includes growing in the grace and knowledge of our Lord and Savior Jesus Christ, which is done through prayer and the study of God’s word, all by the power of His Spirit who lives and dwells within us.
Also, Scripture makes clear that this earth is not our home. Like Abraham, we live as aliens in a foreign land, and we are looking for the city which has foundations, whose architect and builder is God. We are to desire a better country, a heavenly one, and our God has prepared such a city for us (Hebrews 11).
Therefore, we must conclude that in this life, our goal is to glorify God. Some will also be blessed with earthly riches, just as Abraham was, but even then, we do not seek such riches, nor is that our goal, just as it was not Abraham’s goal. Indeed, if we have such riches, we use them for God’s service, just as Joseph of Arimathea used his tomb for the burial of the Lord. Some will not have such riches, as our Lord did not have them. We are to be like Paul in Philippians 4:
Clearly, we can only do this in the power of the Spirit of Christ, just as Paul says in v. 13 above.
Furthermore, we should expect persecution as we live out a Godly life according to 2 Timothy 3:12, John 15:18-20, James 1:2-4, 1 Peter 1:6-9, among others. Persecution is to be expected, according to scripture.
Finally, we also seek God’s kingdom and His righteousness with an expectation not of earthly rewards, but of heavenly rewards. If we have a motivation of pleasing God, He will be pleased with us, and praise will come from Him and not men. In 1 Corinthians 3:10-15 Paul talks about heavenly rewards, so we should live in expectation of them. Only those works that are done with a motivation to please God and not men – works done in the Spirit and not in the flesh – will receive heavenly rewards.