Arguments that use the gender or race of the arguer as a reason to dismiss their opponents are fallacious. They both commit the logical fallacy called ad hominin. This fallacy is when you attack the person making the argument instead of the argument itself. As Christians who pursue the truth wherever we may find it, we should never use this kind of argumentation, and we should never accept arguments that do, even if the conclusion supports our position.
Critical thinking seems to be on the decline. At least, that is how it feels, but I doubt that is the case. It has probably always been this way. As scripture reminds us, there is nothing new under the sun. Poor reasoning is a product of the fall. Sin affects the way we think, and we all struggle with it. In theology, we call this the noetic effects of sin. We are morally compromised, and we will often work to suppress truths that do not align with our fallen biases.
Our propensity to reason poorly is evident today in arguments made for and against controversial topics closely related to gender and race. For example, a man will argue against abortion philosophically, and the opponent will dismiss it because the arguer is male, but arguments do not have genitalia. Plenty of women make the same arguments, so the attempt to dismiss it based on gender is impotent.
Another area where this kind of bias affects reasoning is topics related to race. Many people say that one race cannot speak about the struggles of another race because race A has never experienced what it is like to be race B. Therefore, anytime someone of race A makes a point that contradicts what someone of race B says, it will be dismissed as irrelevant even if it is logical.