Yes, there are objective truths, and I believe them.
Having said that, there are plenty of people that will deny objective truth (erroneously) for the benefit of their personal religious, political, or similar beliefs.
A simple and stupid example: The objective truth is that liquid water is wet. There will be people who would say that it isn’t wet – rather, you get an answer like this (from the Guardian newspaper):
Water isn’t wet. Wetness is a description of our experience of water; what happens to us when we come into contact with water in such a way that it impinges on our state of being. We, or our possessions, ‘get wet’. A less impinging sense experience of water is that it is cold or warm, while visual experience tells us that it is green or blue or muddy or fast-flowing. We learn by experience that a sensation of wetness is associated with water: ‘there must be a leak/I must have sat in something.’