Very much down to competition rules. The standard adult code of rules (SCoR), which has to be adopted by all leagues, states ...
Within the National League System (“NLS”) all matches shall have a duration of 90 minutes. All matches outside of the NLS shall have duration of 90 minutes unless a shorter time (not less than sixty (60) minutes) is mutually arranged by the two Clubs in consultation with the referee prior to the commencement of the match, and in any event shall be of equal halves. Two matches involving the same two teams can be played on the same day providing the total playing time is not more than 120 minutes
So unless the game is in the NLS (details here
https://en.wikipedia.org/wiki/National_League_System) the referee and both clubs can agree to shortening the game, as long as this is agreed before the game commences and the two halves remain equal. If any one club, or the referee, doesn't agree then it stays as 90 minutes. If this means the game doesn't finish then the referee would need to report the facts to the competition, especially if one club's refusal ultimately caused the game to be abandoned.