There’s no one way to be a man.
— ACLU (@ACLU) November 19, 2019
Men who get their periods are men.
Men who get pregnant and give birth are men.
Trans and non-binary men belong.#InternationalMensDay
It's an interesting Humpty-Dumptyism, because it's something that all but a few would have regarded as gibberish twenty years ago and that the vast majority of people regard as gibberish now, and in fact they are right -- on its own, it is gibberish still. Without knowing the account being assumed, there is no way to understand what it's saying. There is no definite commonly accepted meaning to the words 'man' and 'men' as they are being used here, and the word can't be used merely ostensively without being incoherent or pointless. If by 'mockingbird' I can arbitrarily decide to mean 'whatever imitates something else', which strictly speaking I could, then 'Mockingbirds that are not birds are mockingbirds' either means 'whatever imitates something else, even if it is not a bird, imitates something else', which is trivially true but makes no substantive point, or it means 'Whatever imitates something else, even if it is not a bird, is a kind of bird from family Mimidae', in which case it is incoherent. In neither case does it actually say anything about mockingbirds, and you would certainly regard me as speaking nonsense if I went around saying such things without telling you how I was using the term. What's needed is an actual, independently established, account of 'man' that would make the slogans some kind of technical usage. There is no such account, however. Despite the ACLU tweeting this, this is not how 'man' has generally been taken in law, for instance. Nor has there been any attempt elsewhere worth taking seriously.
There has been some work of note trying to work out an account of 'woman' in analogous situations in feminist philosophy; feminist philosophers have from the beginning recognized the above problem, and thus have proposed various projects of ameliorative inquiry or analysis (in colloquial terms, finding a better or more adequate definition or account than the ones in use). The most influential of these is Sally Haslanger's definition of 'woman' as something along the lines of 'a member of a social class that is unified by a particular form of social subordination based on presumed or perceived female role in biological reproduction'. The work of Haslanger and the handful of people who have agreed with this definition to establish has been heroic; I doubt very much anyone could do any better. Nonetheless, it has run into the problem all ameliorative analysis faces: it only pleases those who already wanted something exactly like it. It has not pleased those who want a trans-inclusive definition of woman (because whether you count as woman according to it depends entirely on whether other people presume or perceive you to be, and it would mean that becoming a woman is volunteering for social subordination) and it hasn't really please anyone else, either. It at least has the rhetorical inconvenience that if we started using it, we would have to say that one of the goals of feminism is to try to make it so that there are no women. Even granted that it might be a beneficial improvement in some abstract sense, part of the point was to get a way of thinking about the matter that could actually be used in public without being mocked for self-parody.
Of attempts to go beyond Haslanger, the only work I've seen that even has any serious promise is that of Katherine Jenkins, who argues (rightly, I think) that a trans-inclusive definition of woman has to be in some way a double rather than a single concept. Jenkins's definition is (without getting into technicalities, which can be found in her paper) disjunctive: a woman is someone who is either a target for subordination due to supposed physical features presumed to be indicative of female role in biology or who has a psychology formed to guide them through situations in a way appropriate to such women as a class. I don't think this actually does what Jenkins wants it to do, since the appearance of 'women' in the second disjunct seems effectively equivalent to saying that transwomen are women only in a secondary and derivative sense. The derivativeness might be tolerable given Jenkins's aims; I don't think the secondariness is consistent with Jenkins's aims in the analysis. It also has analogous rhetorical inconveniences, and because of that I don't expect it to be to come into any serious widespread use. I suspect, in fact, that the only way to get the kind of inclusivity Jenkins wants is to posit womanhood as a primitive indefinable with a double exemplification, physical or psychological; and while this is consistent with aims that could be considered feminist, it is not consistent with feminism as actually practiced, for the same reasons that essentialism and the eternal feminine are not popular with actual feminists.
Even if accepted, however, none of this really gives a platform by which one could do something similarly with men; they both would seem to require that becoming a man is deliberately becoming a member of a class that by definition subordinates women, which does nothing to clarify what people in that category are actually trying to do.* If you want 'men' to cover trans and cis as subcategories, you need an account of why the adjective in 'trans men' is not alienans, conveying the sense not of being but of merely trying to be. But that requires actually having a definition that makes sense of everything you are trying to do.
But, of course, the point of the ACLU is neither to say anything true nor even to say anything coherent. It's more like trying to wish something as the definition without actually doing the defining. The point of such slogans is to rally-cry; it's about in-group formation. The whole point is to use a nonstandard usage; there would be no point in going around saying "Men are men, too" if you just used 'men' in the way most people usually do. I suppose they are admirably open about doing it, since they as much as say it with the claim about belonging. The point is to convey something like 'We are in the group that uses 'man' in this uncommon way as a shibboleth for being in this same group with trans and non-binary men, excluding everyone who uses it in the common way.' But using the club handshake is not a substantive position about anything, and doesn't itself solve any real problems.
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* It's not essential to the reasoning, but it is also, I think, contrary to the 'sense of the room' one gets in most contexts. It would seem to make F-M transitioning more problematic than M-F transitioning, the latter of which could perhaps be treated as a kind of solidarity (which I think many trans women do see it as). If you look at transgender conflicts and controversities, however, they are overwhelmingly about trans women, M-F transitioners. There are very few transgender controversies about mens' bathrooms or mens' sports; trans men are not in general seen as a potential threat or as having any kind of unfair advantage in competition.
As another side issue, a problem with all the ameliorative definitions on the table is that they are all passive rather than active; it's pretty obvious that to cover trans cases you'd need the definition to have an active structure, like Ramon Llull's definition of the human being as animal homificans, the humanifying animal, the animal that humanizes itself and other things. You'd need 'woman' to include something that could be characterized as woman-ifying (womanizing is already taken, unfortunately), and similarly you'd need some kind of activity that specifies what it would mean to be man-ifying. But I am skeptical of the idea that you could come up with any suggestions of woman-ifying and man-ifying activity that would be both plausible to people at large and consistent with the ameliorative aims in question.