What does masculinity mean?
The thing that makes some of the core questions -- like "How men can be supportive and non-oppressive while remaining overtly masculine?" -- difficult is that there's a lack of clarity about what constitutes "masculinity," or even what criteria we might use to sort through the question. There are a few obvious answers that we can throw out:
1) Biological essentialism -- This is a non-starter because nearly every alleged biological difference between men and women (or even just cis men and cis women) has, upon further investigation, turned out to be 1) a result of social processes, 2) nonexistent, or 3) statistically significant but practically meaningless (e.g. a 1% difference on some measurement).
2) Extra-human dictate -- A devout adherent of a particular religion might feel that God dictates a particular form of masculinity as the proper one, but this seems like a non-starter in a religiously diverse and atheist-heavy group like the folks discussing this issue at Alas.
3) Tradition -- On the one hand, using tradition to define masculinity requires acceptance of some form of cultural-historical relativism since ideals of masculinity have varied so much (as well as cultural purification so that we know which definition applies where). And it also seems odd for people adhering to a gender egalitarian philosophy to privilege tradition -- as several commenters point out, "thinking about gender" and "being non-oppressive" are traditionally inherently un-masculine activities.
4) Pure definition -- I suppose there may be a few people who value having the word "masculine" applied to them but have no attachment to any specific content, such that if we all agreed to call wearing a pink tutu super-manly they would go buy a closetful of them. But only a few. And this kind of Humpty Dumpty strategy would make the original question vacuous -- it's easy to construct a non-oppressive masculinity if you can just decree that any old thing you come up with is now officially masculine.
An important starting point, I think, needs to be asking people "what does masculinity mean to you?" This would be a question posed both to people who identify as (or aspire to be) masculine, as well as those who find masculinity sexually/romantically attractive.
I suspect, too, that what we'd find is that there is no one definition of masculinity -- and therefore no one answer to Clarisse Thorn's questions. What one person finds valuably manly may have little if any overlap with what another person says. A while ago I read Bond's description of what specifically constitutes her masculinity/butchness -- and I found it an interesting mix of things I do but don't see as contributing to my personal sense of manliness, and things I have little interest in regardless of whether they might be more manly. Bond herself recognizes this sort of issue and is very clear that she's talking about what makes her personally feel more masculine and strongly opposes judging others' gender expressions as excessively or insufficiently manly or womanly.
It's not entirely clear whether I'm among the people Clarisse Thorn is addressing her questions to -- the series is framed as being directed to "cis het men," which certainly describes me, but elsewhere she refers to her target group as "straight/dominant/big-dicked," on which I answer yes, no, and I've never bothered to compare. There are certainly ways that I vary from the prevailing cultural norm of masculinity (to the point that Christina and I joke that I'm the wife and she's the husband), and maybe that would make me un-manly enough (and un-manly in the right ways) that someone like Clarisse Thorn who has a thing for manly men wouldn't be attracted to me, but that has never made me feel that my masculinity is in question in any way. Indeed, there's little that I can imagine that would make me feel less like a man. Certainly I would feel uncomfortable doing a lot of traditionally feminine things, and my maleness may be the cause of that discomfort (I wasn't born liking a shirt and tie better than a lacy blouse), but it's not a conscious justification. That is, I don't take "because it is/isn't manly" to be a valid reason for me to do something. Perhaps this is an expression of deep-rooted privilege -- I've always fit so well into the masculine role, and been able to easily get away with the parts where I don't fit without serious social penalty, that I've never had to consciously work on masculinity. But it does mean that a fortiori feminism has never felt threatening to my masculinity. Certainly I didn't instantly become some sort of super-feminist, and while my current views all fall within the scope of what feminists believe I might still be on the wrong side of some intra-feminist debates. And some of my resistance to some feminist ideas may have been caused by ideals of masculinity that I internalized. But I didn't consciously experience this resistance as aversion to emasculation, nor did I have to defensively construct an alternate masculinity (e.g. along the lines of the oft-suggested "it's manly to fight for gender equality" argument). So in the end it's hard for me to say how to be non-oppressive yet still manly because I have trouble imagining the quest for non-oppressiveness leading me to a problematically unmanly conclusion.