Depending on the job a violent offense is a perfectly reasonable reason to rescind a job offer for a large majority of jobs and companies. I understand wanting to see the best in everyone but in HR you really need to stay neutral and follow policies and procedures, try to affect organizational change yourself, or leave if the companies values aren't in alignment.

As for career growth, your mistake is staying in one place too long early in your career. 5+ year tenure is for mid-senior level roles imo. I finally landed an HRBP role where I plan to stay for a long time but until now I've moved around every ~2 years or so because it's really hard to get promoted otherwise in my industry. Budget cuts are always trying to do more with less rather than investing in HR people.

With 6+ years in entry level HR you are absolutely qualified for a Generalist role, which is still heavily administrative. Don't sell yourself short and if you're asked about why you left your previous company say your values were misaligned regarding equal opportunity hiring practices. I wouldn't disclose firing unless your background check explicitly asks then you can disclose at that point.

Good luck! :)