No threshold approach in the risk assessment of genotoxic carcinogen. Is it still well supported by current knowledge of carcinogenesis?

A large amount of experimental data indicates that carcinogens have actual thresholds, which are related to the saturation of defense mechanisms such as DNA repair and antioxidation. Currently, there is a tendency to be lenient towards those with threshold mechanisms, while being strict towards those without thresholds.

Not supported by original data used to define the hypothesis.

It is not; it has never been 

The no threshold approach in the risk assessment of genotoxic carcinogens was created in recognition of the fact that our tolerance for cancer risk is lower than our tolerance for most other toxicological endpoints.  As a result, we are often setting permissible exposure levels at exposures lower than those at which we can collect reliable data. The argument for linear extrapolation of high dose data to zero explicitly rejected the idea that it was accurately measuring or predicting risk at low doses (https://pubmed.ncbi.nlm.nih.gov/7217854/)  We can measure things that lower the risk of initiating malignancy: metabolism and distribution at the organismal level, DNA repair, apoptosis, etc.at the cellular level.  Knowledge of the existence of these factors is not, in and of itself, useful. The question is whether we can use those measurements to more accurately determine the dose below which the risk of malignancy is below the acceptable limit.  

There is both nonlinear and linear dose response curve for genotoxic carcinogens.A deep insight of knowledge is itself showing both.

The approach isn't obsolete, but it's being refined. Modern risk assessment increasingly incorporates mechanistic understanding while maintaining precaution where uncertainty remains significant.

Absolutely not; all genotoxic carcinogens show nonlinear dose response curves based on current studies. The difference between theory and having actual data.

The no threshold approach is applied