Question: Is truth objective?
Short Answer: Yes. Truth is knowable, observable, testable, and defendable.
A Little More: We can see this in our world. There are certain facts that do not change no matter how we feel about them. An example of this is the reality of gravity. It doesn't matter about your opinion concerning gravity. If you walk off a cliff unassisted, you will fall. This is an objective truth. Another example is mathematics. They do not change. You can try to make 2+2= 5 but, as long as you use the correct rules, it will always equal 4.
The issue is people misinterpret "truth" claims for opinions. Someone can have an opinion about the truth, but it does not change the truth.