How does termination involving conduct impact future public trust background reviews

My employment was terminated for conduct during probation. The conduct issue is questionable. Two employees were regularly giving me a hard time and I pushed back gently and instead offered an olive branch. No warning given and no questions asked, my employment was terminated. This was a public trust position. How long does it impact or bar me from future employment for public trust or other clearances? I believe I read an article that said it might impact/bar for at least five years. Please confirm whether this is true. How can I mitigate the issue on future applications if I am still eligible to apply for other positions?

It really depends on the circumstances. What does “pushing back gently and instead offered an olive branch” mean? Normally pushing back and offering an olive branch are opposite sides of the spectrum.

We were working on a PowerPoint and I simply restated in an email that it met all the requirements for presentation/publishing with the changes that I had made to a prior document. I offered that I was aware that she had worked closely with my predecessor on the project and that I hoped in the future she and I could do the same. The manager took it as a lot of back and forth.