“For to you it has been granted on behalf of Christ, not only to believe in Him, but also to suffer for His sake.” (Philippians 1:29)
Note that faith is granted in this verse. Some believe saving faith is given by God to certain individuals. The NKJ translators interpret the Greek verb as has been granted not given as in forced or compelled upon a person. If faith were given in a compelled or forced way, then a problem develops. God would also be the giver of suffering and persecution per the latter half of this verse.
Charidzomai is best interpreted as granted as in freely offered. Christ offers salvation through His finished work for those who rely, trust, or believe on Him. Of course, along with salvation comes persecution. This privilege of suffering is also something which comes along with our identification with Christ (see the phrase fellowship of His sufferings in 3.10).
Charidzomai is also used in the following passages:
“Now we have received, not the spirit of the world, but the Spirit who is from God, that we might know the things that have been freely given to us by God.” (1 Corinthians 2:12)
“And be kind to one another, tenderhearted, forgiving one another, even as God in Christ forgave you.” (Ephesians 4:32)
It would be difficult to conclude from these examples a compelled idea of the Greek verb. That is, we are freely given things not compelled to have them. Forgiving another is something we certainly decide to do. It is not compelled. I must choose to forgive. If I will not forgive, then my Father in Heaven will not forgive me.
Therefore, Philippians 1.29 does not have to support the idea of saving faith being a gift of God. Some will import this upon the verse to defend a theological filter (We all have presuppositions we defend.). I conclude that salvation by grace is the gift and faith is our response not our work (cf. Ephesians 2.8-9). Of course, I do have a theological bias :)