Why was part of this gravestone redacted, and what would it have said?

~~I deleted my first reply because, after further research, I was completely wrong.~~ Nope, I was right the first time...

Dr. Henry Rutherford Butler was a Past Grand Master of the Most Worshipful Prince Hall Grand Lodge of Georgia, F&AM. He was the 9th Grand Master of this jurisdiction and, as his gravestone reads, he served in this role for 30 years. That's... quite an achievement of dedication and endurance.

Contrary to the conspiracy theorists, there is no worldwide governing body for Freemasonry. The United States includes 51 jurisdictions - fifty states and Washington, D.C. I'll explain the use of this word later.

Unfortunately, Masonic politics are not immune to the biases of society. In the waning years prior to the American Revolution, 15 African American Freemasons joined a British military Lodge but were later rebuffed by the (Provincial) Grand Lodge of Massachusetts due to their race. They then petitioned the Grand Lodge of England for their own Charter, which created African Lodge #459 on 3 July 1776. They became African Lodge #1 when they separated from England to form the African Grand Lodge in 1808, which they later renamed the Most Worshipful Prince Hall Grand Lodge after their first Worshipful Master (president) in 1847.

In the decades since, the "mainstream" Grand Lodges often refused to admit African Americans. As a result, parallel Prince Hall Grand Lodges spread to almost all U.S. jurisdictions. Most "mainstream" Grand Lodges have since integrated themselves and now allow members of any race, as do the Prince Hall Grand Lodges. However, the two-Lodge system has become ingrained in American Freemasonry.

Jurisdiction is a loaded term in Masonic parlance. Each Grand Lodge is sovereign within its territory, known as its jurisdiction. It's typically considered bad form for one Grand Lodge to charter a Lodge in the jurisdiction of another Grand Lodge - for example, there would be quite a few strong words shared if the Grand Lodge of Pennsylvania decided to charter a Lodge in New York. Yet, now we have both "mainstream" and Prince Hall Grand Lodges in the same territory. This dissonance is one of the sticking points now that the Fraternity is (by and large) attempting to heal old wounds, but deep down we're still grappling with the same biases that we were centuries ago. That's the unfortunate difference between ideal and reality.

Relations between Prince Hall and "mainstream" Grand Lodges continues to be a bit complicated. Georgia is one of seven jurisdictions in the U.S. (of 51) that does not have recognition between its "mainstream" Grand Lodge and its Prince Hall counterpart. In layman's terms, the "mainstream" Grand Lodge of Georgia does not consider the Prince Hall Grand Lodge of Georgia to be legitimate, whereas many other states go so far as to allow Freemasons of either group to attend each others' meetings and otherwise mingle within the Fraternity. The most recent example of mutual recognition is from the state of Florida.

Once again, what does this have to do with a tombstone?

This time, I'll admit that I don't have a good answer. I would now guess that the excised section once read "Prince Hall". I'm not sure why this would be removed - the work appears too clean and careful to be vandalism. It's possible that the tombstone was designed to conspicuously omit these words, leaving only "Free and Accepted Masons". To me, this evokes a noble sentiment of the universality of the Fraternity.

EDIT: I was incorrect about being incorrect - that's what I get for second-guessing myself. u/blfstk and u/anowlcalledjosh had it right.

I've put in a few inquiries and will let you know if I learn more. Here's the official story.