I love these sorts of discussions, because they depend so heavily on what presumptions people bring to the table. So let me set up some postulates.
If there were no God, there would be no objective morality, one existing irrespective of whether there were humans aspiring to it. There might be a moral standard subscribed to by all or most sane humans, but it would be dependent on the common consent of mankind, a product of their consensus as to what is good or evil.
For the remainder of this post, I am going to postulate the existence of God -- a God ontologically prior to the Universe He created, and self-limiting (that is, He is effectively omnipotent, omniscient, etc., and nothing outside Himself limits what He can do or know). Further, this God reveals Himself to mankind under the Persons of Father, Son, and Holy Spirit, and the Son persona became incarnate as Jesus the Christ. (We won't go into Trinitarian theology or Christology for this, just presume orthodox Trinitarian doctrine as background for moral theology.)
Now, allow me an excursus for a parallel that may illuminate the point I'm making. Newtonian physics presumes that all matter has inherent characteristics including mass, which is absolute. I.e., if you take a ten-pound rock and chip or abrade away three pounds of it, you have a seven-pound rock -- but you also have three pounds worth of flakes, pebbles, rock dust, etc. Same ten pound, redistributed.
Einsteinian physics says this is relative, that accelerating that rock to high speed makes it mass more. Newtonian physics is true for objects at rest, but is a special case within Einsteinian physics, and relativistic mass is as "real" as rest mass. Something moving so fast its mass doubles behaves as though it weighed 20 pounds, not the 10 pounds it would mass at rest. All the characteristics of an object are relative, based on its speed and the frame of reference you measure it at.
But Einsteinian physics does have an absolute -- the value "c", the speed of light in a vacuum. The Newtonian "absolutes" vary relative to this single Einsteinian absolute, hence "relativity" for Einsteinian physics.
Now, where I am going with this is that when people begin speaking of objective, absolute moral standards, they hold up things like no sex outside marriage, no theft, etc., and deem them as moral absolutes, referencing God's commandments in Scripture as validation for them.
But when Jesus is asked about such matters, He refers us to three specific points -- and they're not the ones usually spelled out by the "objective morality" arguers.
34 Hearing that Jesus had silenced the Sadducees, the Pharisees got together. 35 One of them, an expert in the law, tested him with this question: 36 "Teacher, which is the greatest commandment in the Law?" 37 Jesus replied: " 'Love the Lord your God with all your heart and with all your soul and with all your mind.' 38 This is the first and greatest commandment. 39 And the second is like it: 'Love your neighbor as yourself.' 40 All the Law and the Prophets hang on these two commandments." (Matthew 22:34-40, NIV)
So in everything, do to others what you would have them do to you, for this sums up the Law and the Prophets. (Matthew 7:12, NIV)
These are God's absolutes, as spelled out by one Person of the Godhead. How they work together is defined in Matthew 25:31-46. "Inasmuch as you have done it unto one of the least of these, you have done it unto Me."
This sounds suspiciously like Fletcherian situation ethics. But it's not quite the same thing. Like the "absolutes" of Newtonian physics, the standards of the "objective morality" crowd are valid -- within a specific frame of reference. That frame defines most of human behavior. Sexual license is not excused or justified by a slippery Fletcherian situational approach. But when the application of the legalistic absolutes clashes with the application of the Two Great Commandments and/or the Golden Rule, then they come into play, and supersede the specific application of the Law to the particular case at hand.
The Two Great Commandments and the Golden Rule together constitute the "speed of light" for God's objective morality. The code of behavior that is usually deemed "objective morality" is true in most cases, just like Newtonian physics is. But when it collides with the Law of Love, it must give way to God's own absolutes.