Why is this hobby, which has so much to recommend it, overwhelmed with furries and social outcasts? RPGs bring in language skills, mathematics, tactical planning, social activity and imagination. They're a great hobby. Why can I not run a game without men with anime backpacks and women who clearly hate themselves appearing, thinking I am their people?
How to solve this problem? I've all but quit the hobby due to the sorts of people who show up.
The easiest way to avoid such people is to not play in public/pick-up games at your LFGS or online, and instead only play with close friends (and their friends, and so on.) If none of your current friends are interested in or have any experience with TTRPGs, it is likely that you do share some interests that are adjacent to the hobby (whether it be video games, history, fantasy novels, comic books, metal music, etc.) You can leverage these interests to try and convince them to try out the hobby itself...though this assumes you're willing to GM and that your friends are actually your friends, and are willing to enjoy your company for 4+ hours every two weeks.
If you don't actually have any friends (like many users of this website) and are unwilling to make new ones, then I can only advise you on how to avoid the sorts of individuals you speak of, when playing with strangers online or IRL.
To preface, the majority of these individuals belong to one of two types:
A) Degenerates that have managed to find or form a like-minded group of fellow degenerates with which to indulge in ERP and/or other assorted masturbatory OC donut steel wankery behind closed doors, who go on to have infinitely more fun than either you or I will ever have in this hobby. These types are very easily avoided and often go unnoticed unless they openly discuss exploits that occur within their games, often shared in the form of fan-fiction or DeviantArt-tier illustrations involving their group's gallery of fetish-laden Mary Sues. They tend to have groups that stay together for years, only to split apart due to social drama (often involving polyamorous relationships or political sperging.) These groups often play a wide variety of systems, and can sometimes form when several individuals of the second type come together and realize they share similar tastes. Every FLGS or local community I've been involved in has one or more of these groups, with some becoming infamous amongst the local scene, and most going largely unnoticed (aside from their stench, or obvious online red flags like profile pictures.) Your only chance of crossing paths with these people is if you join random games online without vetting any of the people involved (as these people are fairly easy to suss out IRL), and most memorable horror stories about TTRPGs come from somebody inadvertently joining one of these groups.
B) This type consists entirely of spergs who either haven't made the proper connections to join the first type in their games, or that are so irredeemable as to be shunned from even those circles. Everybody in this hobby who has played with strangers for any significant length of time has encountered this type, once referred to as "That Guy." Every FLGS or online community has one or more of these people, and they are either actively shunned or at worst placated in the interest of keeping things civil (or because they pay money to whoever is in charge, typically the owner of a FLGS.) Avoiding this type is difficult but not impossible when playing games with strangers, and basically requires that you (or the GM) extensively vet every possible player. If playing online, use a shit test that involves basic reading comprehension on the part of players when submitting applications to join your game (such as "to confirm you read this in its entirety, please say X in your application") as this will filter out a surprising number of undesirables. From there, check the individual's profile for any obvious warning signs, then see if their username can be linked to anything online that might indicate if they may be a problem or not. For IRL games, it becomes a bit trickier, as most FLGS will frown upon groups that reject players from their games for what may be perceived as petty or non-inclusive grounds. To make matters worse, these people are often kicked out of groups at alarming frequency, and are constantly on the lookout for new ones to worm their way into. Note that this applies to any hobby at your FLGS, not just RPGs. It is for this reason I do not advise attempting to play with strangers IRL at your FLGS or other communal space if you want to
absolutely guarantee avoidance of these people, and instead only advertise at these places, while planning to actually play at your or another players house (which has its own associated risks.)
I should also touch upon the boilerplate advice of "have you tried not playing D&D?" as well, because it is commonly believed that most of these people only play popular systems. In my personal experience, this is no longer the case. During the days of 3.5/PF1e this may have held somewhat true, but ironically the corporate-sponsored messages of tolerance and inclusivity attached to 5e D&D and neighboring spheres has somehow had the opposite effect when it comes to actual degenerate players. Sure, you're extremely likely to find them in 5e games, as it is the most popular system by a wide margin, but you're practically
guaranteed to run into them if you try to play something more "niche." I think this is partially thanks to niche systems being much more accessible to the average person than they used to be, due to digital distribution and the ease of .pdf piracy. This means people can more easily find systems that conform to their tastes (degenerate or otherwise), rather than homebrewing D&D to do it for them (which was rampant in 3.5, but still popular with 5e.)
When it comes to choosing a system expressly to avoid these people, I've found that the more grounded in reality or "simulationist" a system is (whether it be in rules or setting), the less of them you're going to find. Games like Delta Green, (most) OSR-adjacent games, early editions of D&D, FFG 40k RPGs, WHFRP, Call of Cthulhu, Twilight: 2000, any historical-bsaed system, etc. will all attract different types of autists on their own, but very rarely are they furries, weebs, or (blatant) fetishists. There is an exception for simulationist universal or generic systems like GURPS, however, as the ability to play anything you want will obviously attract people who will take that as an invitation to play a 10 foot tall nonbinary cow person with 6 dicks that shits from their nipples.
Lastly, as to why exactly these people seem to be so prominent within TTRPGs and related hobbies? Tabletop RPGs, Miniature Wargames, TCGs, Board Games, etc. are all intrinsically "nerdy" hobbies, but unlike most other "nerdy" hobbies they actually involve sitting in a room with other people for hours at a time and sharing each others company. Statistically speaking, your chances of encountering these people at your FLGS are the same as encountering them on a forum like this one, when playing an MMORPG, or when playing a game on Roll20. The main difference is that by
seeing them IRL, you are alerted to their existence, but they have always been in these spaces and will continue to proliferate here unless properly shamed for their behaviors or instructed to behave otherwise. The problem is that the community has since stopped doing this, due to the hobby having been co-opted by various movements and ideologies as an inclusive safe-space where your imagination can run wild, so long as nobody gets triggered and has to pull out their X card. The popular narrative that this hobby has always accepted social exiles and degenerates of various stripes is only true to a certain extent, as the worst of them have always eventually been excluded or outright shamed and ridiculed, and this has been true since the hobby's inception.
TL;DR: Much like masturbating, you're better off not doing it with or around strangers. You can always try and convince friends to do it with you, and if that doesn't work just try doing things solo. And don't forget the lube!