Is it that these are more natural?
(e) Be yourself, no matter what others (may) think.
(f) Be yourself, regardless of what others (may) think.
Is "may" optional? Would "will" be used instead of "may"?
When I wrote "for all of these" in my previous post, I was referring to
all of (a), (b), (c), and (d). In other words, my recommendation to replace the "whatever others ... think" part with either of the two alternate phrases I suggested
is applicable to all four sentences.
As for your new questions, "what others think", "what others may think" and "what others will think" are
all OK to use, but they have different nuances. For example, "what others will think" implies something that will happen in the future, whereas the other versions do not have such a strong implication of a future occurrence.
I think that the version with "may" is the most natural, but you can use any of them.
When you ask these kinds of questions, think about Japanese. Surely the same thing is true where there are multiple different ways to say things, any of which might be said by a native speaker, but some versions are more natural or sound better than others. All languages are like that.