The 4th definition in Merriam-Webster’s dictionary for love is probably the best usage for biblical love for one another.
It states love is…
unselfish loyal and benevolent concern for the good of another: such as (1): the fatherly concern of God for humankind (2) : brotherly concern for others
Unselfish and benevolent concern for the good of another or the desire for the best for someone else.
The most benevolent concern a Christian can have for another is the hope of salvation through Jesus Christ, therefore, the love of another from a Christian must balance with biblical truth.
Secular society through moral relativism has forced the idea that to love someone you must agree and confirm everything they are about.
This kind of love cannot coexist with biblically based love because there are times people do things that do not meet biblical morals.
That doesn’t mean that love is not present.
In John 13:34-35 Jesus said…
34 “A new command I give you: Love one another. As I have loved you, so you must love one another. 35 By this everyone will know that you are my disciples, if you love one another.”
Throughout the Gospels Jesus points to the morals of the Old Testament and commanded us to follow them.
In Matthew 4:17, He commanded us to repent, in Matthew 4:19, He commanded us to follow Him, in Matthew 5:27-30, He commanded us not to lust, and in Matthew 28:19-20, He commanded us to make disciples.
He commanded us to love, but to do it honestly and we cannot love honestly if we justify sin.