Incel comes etymologically from "involuntary celibate", we know that. But the current consensus on the term in this time of identity politics is a different one:

An incel is part of an online community that has negative opinions about "women" as a problem and advocates for bad behaviors towards them and also resents men and women who are in a relationship.

So this is a specific flavor of a sexist person and not a person with no girlfriend. This person can be a sexist even with a girlfriend. On the other hand, these huge percentages of men on the lookout for a girlfriend can't be all so sexist.

If someone calls you an incel, for talking about men's rights, you should not entertain that, regardless of your relationship status. An incel is a person who hates women, neither a man looking for a girlfriend nor a person who talks for men.

enjoy your day!

According to Wikipedia:

The subculture is often characterized by deep resentment, hatred, hostility, sexual objectification, misogyny, misanthropy, self-pity and self-loathing, racism, a sense of entitlement to sex, blaming of women and the sexually successful for their situation (which is often seen as predetermined due to biological determinism, evolutionary genetics or a rigged game), a sense of futility and nihilism, rape culture, and the endorsement of sexual and nonsexual violence against women and sexually active people. Incel communities have been increasingly criticized by scholars, government officials, and others for their misogyny, the endorsement and encouragement of violence, and extremism. Over time the subculture has become associated with extremism and terrorism, and since 2014 there have been multiple mass killings mostly in North America perpetrated by self-identified incels, as well as other instances of violence or attempted violence.