In a way the cultural exchange program is a necessity for the slice-of-life setting. More of the commonly accepted lore with monster girls in the contemporary moment is that they entered our world through the magic of their demon lord (the one who transformed all of the monsters into their current female form), something akin to the plot from Gate - Jietai Kare no Chi nite, Kaku Tatakeri. Their really is no support at this time that shows whether people knew about the species of monster girls now found amongst mankind or not. I chose this line of thinking because if monster girls were spirited to our realm through the demon lords power then that would explain the king and knights that the centaurs harp about. It would make the most sense.
I would think that Okayado is following the third of the four options that monster girl enthusiasts usually follow with MG to human population: With mankind at a whopping 90% to the much smaller 10% monster girl population. Going by these stats it isn't impossible that their are just not many monster girls and they are getting by through meeting men that their hearts go doki doki for, rather than for equalization of population. It seems, from the general reaction to the girls in public places, that many people are usually mildly surprised at their existence as is. Marginalization is bound to crop up, but for the most part I don't that Okayado will show any of it unless for a specific purpose.
Furthermore, the internet and other social media is within the MonMusu universe so I will assume that since the monster girls were recognized as peaceable and willing to integrate with humankind that many people know of them, but they haven't actually been in contact with any. Rumors and myths would have definitely cropped up at the beginning or integration into human society, and from that judgemental couple we see that some people still hold that xenophobic/anti-monstergirl attitude. But, to reiterate, I am pretty sure that what we are missing is just further setup and backstory from Okayado here in regards to how monster girls were introduced to the human world (unless they were already there prior and somehow were hiding on an island which would be absolutely ridiculous).
Your second question is actually kind of easily answered. Monster girls, and this is canon, have kidnapped men for copulation or just sex in general. Straight up (though I am not really up in arms against it, this is just a reality made by Kenkou Cross and perpetuated by a wide majority of enthusiasts). There enough males on this planet that a group monster girls could overwhelm a few and continue the existence of their species, as seen by Miia's villiage plan to literally use Kimito to impregnate as many lamia as possible as a shared husband. Though I don't know how exactly the author would go about the migratory nature of harpies, I am pretty sure that within their natural habitat many monster girls would be nearly undetectable by the average person and would not try to raise suspicion up until the point the Human-Monster Girl laws/integration became general knowledge (especially if we go along the lines that they were magically introduced to our world).
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@SanoBaron, what you are referring to, technically, are just beastmen. Okayado seems to be fusing MG canon with D&D stylings in a way. This really just serves to reinforce the idea that the MGs and other species were introduced via magic. But since this story is in media res, I can't say for 100% that there aren't more male species. Okayada never said that he was following Kenkou Cross' canon so it is a possibility that there are species that have males. Its hards to make heads or tails of Okayado's background considering we only have snippets or general facts.
I mean I could do my best to answer any of your questions that you might have. This is an area of my own expertise, but even I don't have all the answers. People deviate from the Monster Girl Encyclopedia all the time. A lot of what Okayado is doing now is along his own personal vision of MG and human interactions in a modern setting. It often does come down to the author's personal structuring. I personally don't stray too too far from KCs MGE but there is stuff within it that I find of little worth (especially in the cookie cutter personality department). Variance among characters, character development, background information, and plot is what really drives monster girl literature/doujins/manga. The fan service and lewd nature of the content is important but not always necessary from what I have seen as well. Its very subjective and the entire concept is interesting and worth delving into.