Is it rude not to attend courses which have no attendance requirements?
I think the question is not "Is it rude?" but "Do lecturers find it ok?" as the answer to the latter is not universal but varies a lot.
Here is what I think about students skipping classes: Personally, I also do not have any attendance requirements (actually, where I am it is currently forbidden to have such requirements) for my classes and there are students who skip some or most classes. Since I do not have such requirement, I am not mad at them, but I note that they miss opportunities to get into a dialogue about the contents which help them learning the material deeper. I do get mad when these students come to office hours asking for clarifications of stuff I treated in the lecture since this basically amounts to unnecessarily teaching the stuff double. When I note that students skip many classes I get thinking "Hmm, let's see how they manage to grasp all the material…". When it comes to exams and I note that the students missed some point which has been stressed in the lectures over and over, I feel like the students really missed a crucial point (even if it is just one) just by skipping the lectures and I do not give any benefit of doubt. It's like "it was obvious that I considered this to be a central point, and you did not get it - sorry for you." However, some bright students that skipped classes managed to impress me during an exam and scored great grades.
As for not greeting students: If you haven't shown up in classes that often, your face may probably not be that familiar to the lecturer… Here in Germany we often have hundreds of students every semester so it is impossible to know the all students who are enrolled but did not show up.
As for the question What can I do to turn it around?: Show that you learned a lot by being great at exams and show that you deeply grasped the material. Do not go to office hours with questions that have likely been answered during the lectures.
To begin with, start going to classes. Your professors have assumed that you are an adult, mature enough to understand what is important in life. Further, they likely believe their classes are important to your degree, or they wouldn't bother with them. (Professors at that level have a great deal of influence over the curriculum.)
As others have said in the comments, not taking attendance does not necessarily mean attendance is not expected; it depends on the culture, the regulations of the institution, and the expectations of the individual professors.
Is it legit? Consider that the first professor didn't "give" you an F. He gave you an examination, which you failed. You earned that F. As for the other one, I'm not sure I understand "try to" say hello. If you're passing in the hall and he ignores a "Hi," then it's safe to assume he's preoccupied, or perhaps irritated. If, however, you're trying to engage him in smalltalk, you should assume he's busy.
To try to turn things around, call on each professor during office hours. Apologize for being absent, and ask whether there is anything you can do, other than studying the text(s) and talking to classmates, to learn the material you missed. Then show up for every class.
The short answer is Yes, at the PhD level, not attending courses is rude. At a guess I would say that these professors do not have a specific attendance policy because their experience is (a) at the graduate level, the students are motivated to be there and they don't need a formal policy to drive home the fact that (b) attending class is an important part of mastering the material and becoming part of a learning community.
You say that these professors know you and see you in the hall every day. I assume you know what you are talking about, and since this is a PhD program these are not large courses and your absence is noticed by everyone, including your fellow grad students, who probably resent you for not showing up. Let's assume that your read of the situation is correct, in terms of the professors knowingly and intentionally acting in certain ways towards you. Since you believe that "There is no explicit attendance requirement" means "I do not have to show up if I don't want to", Professor 1, without revising her syllabus, decided to show you that (a) you are missing things by not showing up, and (b) if you're going to fall back on the letter of the law, the letter of the law says I can ask you anything I covered in lecture on an oral exam. Professor 2 is letting you know that if you don't have time for him, he doesn't have time for you.
I will finish with your question of "What can I do to turn it around and convince people that my intention was not to offend them?" But first I want to address (a) your graduate program, and (b) the purposes of attending class other than learning the course material.
You have clarified in the comments that these two courses cover material which you are already quite adept in. Assuming you know what you are talking about, then you just may be in a program that is a poor match for you, because they are not working with you to structure the program to your interests and capabilities. If that is the case, you have to decide whether to try to get into a program that is a better match, or to get the most you can out of the program you are in. Getting the most out of it would mean repeating some material you already know, but trying to go deeper in your studies. This would require communicating with the professor about your preparation, asking whether you can demonstrate your competency, and then asking whether you can take the work in a more advanced direction. This does create a certain time demand on the part of the professor, so they may not be willing to do this, but you should still do your best to impress them with your competency and maturity. If you are not willing to leave the institution, you may just have to grind your way through a handful of uninteresting courses, which may not be fun, but will at least be easy. Try not to yawn in class.
Beyond that, attending class, especially at the PhD level, is also a way for your professors to get to know you personally, learn what your interests are, and possibly figure out if they would want to work with you. It is also a way for the PhD cohort to bond--an important part of having required courses early in a program and in a fixed sequence, before students move into more specific research interests. Even if you know the material, you could be helping the other PhD students learn it, both by your insightful contributions during class meetings (which hopefully are not just straight lecture) and by working with them on assignments outside of class. If you intend to go into academia, this is an opportunity for you to learn to be a teacher, possibly helping the other students learn material that they may find more challenging than you.
If you want to stay at this institution, want to start attending classes (this is important--you're not getting out of this with "I'm sorry I hurt your feelings but I'm still not coming to your class"), and you agree that these there are legitimate reasons to attend a class beyond just being an information-delivery system, then you need to sincerely apologize to the professors involved and let them know that you intend to change your behavior (i.e. come to all class meetings going forward). I would start out with a written apology and then request to schedule a time to meet to discuss the course. I would try to avoid making a claim that you already know the material, which obviously Professor 1 doesn't believe, and doesn't seem to be the issue with Professor 2. You might say something like you have always worked independently, and thought that the lack of attendance requirements meant that you could treat the course like an independent study. You of course now realize how disrespectful you were being towards the professors, and you apologize for acting like an undergrad. You reiterate your intention to attend all future class meetings, and ask if there is anything else they would like you to do to demonstrate your commitment to the course and to the PhD program.