From A Theology in Tension:

1 John 5:10-11 states: “Whoever believes in the Son of God accepts this testimony. Whoever does not believe God has made him out to be a liar, because they have not believed the testimony God has given about his Son. And this is the testimony: God has given us eternal life, and this life is in his Son.” [NIV]

…

Because as mentioned in verse 10, the unbeliever is calling God a liar, in that he or she refuses to believe in God’s testimony, namely, that which “God has given about His Son” (vs.10). If this were not so, we are left with the absurd notion that John is condemning unbelievers for calling God a liar because they refuse to believe God gave His Son and the gift of eternal life to elect Christians only!

It is clear John is not condemning unbelievers for calling God a liar because they refuse to believe God has given His Son and the gift of eternal life to some select elect, but rather because they refuse to believe God gave His Son and the gift of eternal life to them.