Candidates are rejected when required!
The requirements for Masonry are clearly stated on the web sites of most of the Grand Lodges in the USA. The requirements are simple:
-Male
-Mature of Age (18 some states, 21 most states)
-Belief in God
-Good moral character
-Some states have a residency requirement. Georgia requires three years, California one year, Kentucky only requires that you be a resident of Kentucky. I belong to a lodge in New York state, and I have never lived there)
When a man submits an application to Masonry (called a "petition"), the lodge will assign an investigation team to check on the applicant's background and character. If it is revealed that he has a felony conviction, he does not meet the requirement of "good moral character". If he is wife-beater, a drug user, or an immoral person, then he is likewise an unfit candidate for Masonry.
If the committee determines that the candidate will not be worthy to be initiated into the fraternity, then his application will normally be rejected, without a vote by the lodge as a whole. The Worshipful Master has the option of proceeding with a vote, at his discretion.
Voting is done by the whole lodge. White balls accept, and black cubes reject. (The term "blackball" is generic, most lodges use black CUBES so that there will be no confusion about the vote).
If there is one black cube in the ballot box, the vote is re-taken, as there might have been a mistake. If, on the second ballot, there is a black cube present, then the lodge is asked, who cast the rejection. The individual is required to rise and state his objection to the candidate. The rejection must be a valid one, that did not come up in the investigation. If there are multiple black cubes, then the candidate is rejected immediately.
Becoming a mason is a serious and life-long committment. The process is designed to be difficult, to ensure that the membership is composed of good and ethical men. Only the highest quality of candidate is acceptable.
Hope this answers your question!