The fact that she was part of a coordinated (if poorly) attack on the government for the purpose of trying to stop the peaceful transfer of power would negate that status. She was there, trying to climb through a window that had been broken by the insurrectionists. She was told to stand down and warned repeatedly. She failed to comply and the officer had no other recourse than to fire or allow the insurrectionists into the chamber.
Certainly the incident and other details of her life and behavior, show a person who was more susceptible to becoming a right wing fanatic. Prone to anger and impulsively violent, fits within the spectrum of behavior fo someone susceptible to right wing ideas.
Saul of Tarsus persecuted Christians zealously as a Roman citizen he ruthlessly hunted down and killed them. Supposedly, he received a vision of Christ and became Paul the Apostle, zealously spreading Christianity until he was killed by the Romans. He was a bad man, who became one of the most important martyrs of Christianity. It isn't the character of the person that makes them a martyr, it is what they died for.
Ashli Babbitt died trying to violently overthrow the government because the person who lost, and others, convinced her that the election was stolen, when it clearly was not. She may in fact be a martyr to the cause of White Supremacist insurrection, but that is not a worthy or acceptable cause. Much like there have been martyrs for the Nazi cause in the 1920's and 1930's. They are forgotten or reviled because the cause they died for was evil. Babbitt is not a martyr for any worthy or noble cause regardless of whether she was an entirely decent woman or she is the complex, seemingly erratic, impulsive and potentially violent person we are beginning to see.
The problem that we have in our society, is that we seem to need our heroes to be "purely good" and our villains to be "purely evil". People are complex. The information about Babbitt, makes sense based on what we know of her end. We would figure that someone like her, might be more prone to join right wing circles and end up in a violent attack on the government. Though, there are other people out there who have similar experiences in life and did not join right wing groups, did not attack the Capitol, and lead decent lives.
The reason people are trying to portray her as a martyr is so that they can continue to push the lie that their cause is just and correct. We can push back on that narrative without necessarily having to assassinate Babbitt's character in the process.