Is it possible that God permits or allows people to reject His free gift of salvation rather than what amounts to forcing them to believe?
We all agree that not everyone will be saved.
Yes. God has two wills: a perfect will, unchangeable, eternal, infinite and absolute. He never negotiate His perfect will; and a permissive will, through which God allows things to happen, including the acts of Satan.
People don't reject God's free gift of Salvation because they chose so, they reject it because they cannot see the good within, nor are they aware of the alternative consequences. Only God can "open" the eyes and ears of people to understand what the free gift is.
Mankind, through the choice of Adam and Eve, is doomed to follow the path to eternal destruction.