If objective truth is “a widely held position in academic philosophy” then one should be able to clearly state what this widely held truth is.
I have seen this many times. The reason this happens: a person confessing that they believe in truth only to turn around and functionally deny it, is because they are trying to posture out of the ramifications of having to live with the consequences of holding that truth is subjective. But once a person claims that all logic is “constructed” they have reduced all their knowledge to the solipsism of their construction. It’s a matrix they cannot exit.
What’s tragic about this is that it’s actually an ignorant inversion of reality. The truth is that Logic is the matrix we cannot exit when it comes to knowledge.
The problem is that philosophers want it both ways. They want to be able to appeal to truth when it supports the beliefs they desire, and they want to be able to reject it when it refutes the theories they love. (Oh how this reminds us of theology!)
But it’s simple. If the truth exists, you should be able to clearly state what it is and demonstrate that the substance of your statement is true. After all, there is a reason why you believe that truth exists. If you reject the existence of truth, then you shouldn’t be like religious hypocrites, but should realize and accept the fact, based on your subjectivity, that you don’t even have the ground to object to what is being stated here.