"Most commonly, nihilism is presented in the form of existential nihilism, which argues that life is without objective meaning, purpose, or intrinsic value." (wikipedia)
The thing is: there is no point in the universe. It doesn't exist for a reason, it just exists. There is no rational underlying basis for doing anything at all.
You are.
If the goal is not rational, then the actions are only marginally rational at best. If, for example I was driven to spend the rest of my life wandering round dressed as a giant chicken, well, it would a stretch to call the endavour logical.
If that was your goal, then yes, working towards that would be rational.
From wikipedia:
"Determining optimality for rational behavior requires a quantifiable formulation of the problem, and making several key assumptions. When the goal or problem involves making a decision, rationality factors in how much information is available (e.g. complete or incomplete knowledge). Collectively, the formulation and background assumptions are the model within which rationality applies. Illustrating the relativity of rationality: if one accepts a model in which benefitting oneself is optimal, then rationality is equated with behavior that is self-interested to the point of being selfish; whereas if one accepts a model in which benefiting the group is optimal, then purely selfish behavior is deemed irrational. It is thus meaningless to assert rationality without also specifying the background model assumptions describing how the problem is framed and formulated."
Given that there is (by your own admittance) no basis to call one goal more valid than another, a goal in itself cannot be irrational unless it conflicts with other goals pursued simultaneously.
Finally: I take it that you agree on the original point that caring about whether you are seen as weak by your peers can be (and often is) rational, given your silence on the topic.