In first few minutes of this lecture by Nathaniel Craig, he explains the idea of Dirac naturalness in the following way.
Let us consider a QFT as an effective theory with a UV cut-off $\Lambda$. Let $\mathcal{O}$ be an operator in the theory with a scaling dimension $\Delta_{\mathcal{O}}$ and which appears in the Lagrangian as $\mathscr{L}\supset C_{\mathcal{O}}\mathcal{O}$ with $C_{\mathcal{O}}$ as some coefficient. Then according to the lecture, the idea of naturalness is the expectation that $C_{\mathcal{O}}$ would be given by $$ C_{\mathcal{O}}=O(1)\times \Lambda^{4-\Delta_{\mathcal{O}}} \tag{1}$$ in spacetime dimensions $d=4$. Apart from the dimensionless $O(1)$ factor the rest is plain dimensional analysis and $O(1)$ is some number of order unity.
Does it mean that perhaps Dirac naturalness was not well-motivated and should be sacrificed in favour of technical naturalness? Because as @knzhou points out here, every dimensionless Standard Model coupling would then be unnatural in the Dirac sense.
I also could never sincerely follow the idea of technical naturalness expectation. The idea is that it is possible for a parameter $C_{\mathcal{O}}$ to be much smaller (in violation to Dirac naturalness) if there exists an enhanced symmetry of the theory in the limit $C_{\mathcal{O}}\to 0$. This case is stated as $$C_{\mathcal{O}}=S\times O(1)\times \Lambda^{4-\Delta_{\mathcal{O}}}$$ with $S\ll 1$. What is the justification for technical naturalness or why is technical naturalness expected?
The usual justification given is as follows. If in a theory $C_{\mathcal{O}}$ were really zero and it has some enhanced symmetry, quantum corrections would respect that symmetry and would not generate the operator $C_{\mathcal{O}}\mathcal{O}$. Now, if the symmetry is violated by a some amount $S$, the corrections must be proportional to $S$. If $S$ is small, corrections are small. But how could we know that $S$ is small? It is really a statement about unobservable bare parameter. See this.
