If you have found friends to play with that you enjoy spending time with, it has embraced you. The fact that you may not enjoy going to cons doesn't take away the positive aspects of what you have found in the hobby. Not everyone is going to enjoy going to cons or the public spaces this thread is talking about for a wide number of reasons; it's been a while since I've seen precise percentages, but most games still occur in the privacy of people's homes for a reason. I've been to just enough of them to know that I have no particular feelings about them one way or another (if one is happening close by, and I have some free time, I'll go, but I don't make plans around them), and I participated in organized play leagues for as long as I did only because they were my only real option for playing for many years. I never felt particularly unsafe, but I can fully understand never really feeling welcome.
It's not that I don't enjoy going to cons: I have shyness issues and don't like being around big crowds, so I've never actually been to a con. However, I have had discussions (mostly online discussions) with other gamers who have suggested that I would really like it if I attended a con. I don't think they were intentionally trying to mislead me into something that I wouldn't like (though it's certainly possible they could have been inaccurate while also being genuine).
I also have a friend who shares my interest in anime, and he's suggested that I would really enjoy going to an anime convention: he's even invited me to attend one with him before. I declined mostly because my work schedule conflicted with the convention date, but I would have had to do a lot of prep work just to feel mildly uncomfortable around crowds that big. And that's before I found out about the harassment and assault issues at cons (issues which are probably even worse at anime cons given the increased number of cosplayers, the busty anime characters, the existence of the various genres of hentai, etc).
However, for all I know I might actually enjoy attending a con, and maybe getting to play with one or more of the people I've spoken to online. I'll never find out though, because I don't think it's right that my cost of admission would also have to include my dignity and my right to go unmolested. Just going by what I've read and been told, I couldn't even imagine standing up and leaning over a gaming table at a con to get a bird's-eye-view of a battlemap and not being preoccupied with the possibility of being groped, or of someone taking an upskirt photo or video. And that's me I'm talking about: I don't wear very short skirts, and unless I'm alone I'm never going to be the most attractive woman in the room.
Playing in public is really fun in a lot of ways, but I can fully understand when people say that there is a lot about it that could stand to be improved. A lot of gamers unconsciously form habits they don't realize, and trying to publicly confront them with treats and warnings rarely goes well. Most effective change in this community comes slowly and indirectly. Direct changes like those supported in this thread, however well intentioned they may be, usually backfire; that's why I agree with the sentiment, but not the approach or the forcefulness many want to apply. If the gaming community has a larger problem than much of society, it's because we tend to be far more stubborn, and tend to meet force with equal force, leaving little room for direct change.
My current group actually plays in public (at a 24/7 restaurant). It is fun, and they're welcoming enough because we tip well and don't require much attention beyond the odd drink refill, but I do occasionally have to remind the players to quiet down a bit, or to steer clear of certain subjects. I have to remind myself of that as well, because I enjoy darker humor and lewd (but not vulgar) jokes: I'd probably rate my sense of humor at a middle to hard R. That said, I manage to keep myself to an overall PG-13 rating when I'm in public, because those are the manners I was raised with.
As far as changes proposed in these threads go, some are probably extreme, some are probably dismissive, and many are probably in between. The only proposition that people seem to agree on is this:
1) Don't harass/assault others yourself.
2) Be more aware for harassment/assault going on around you
3) Don't tolerate harassment/assault when you see it
4) Cooperate with security and/or police when asked about harassment/assault that you witnessed
And that's all well and good, but does self-policing like that really work? I've met a lot of good people in this hobby, and I've met my share of awful ones too. I've seen several posters say they wouldn't tolerate that behavior, but I've seen next to nothing about cases where they actually saw it and did something about it (even if it was just calling the harasser out for being a jerk). With the way people are in general, I don't even know if most people would care if it happened right in front of them (unless it was happening to a spouse, sibling, child, or friend). For all I know, I could be groped (or be the subject of one of the other players taking a downblowse photo or video) while leaning over a battlemat at a con only to have the rest of the table do nothing, ask the guy for copies of the photo/video, or tell me it was my fault for wearing a loose or low-cut blouse. And with the way people are in general, I wouldn't put any of those reactions past them.
My best advice is to not focus on the aspects of the hobby that you don't enjoy. For all that I am sure the details are different, what I copied pretty much describes my relationship with the hobby for a long time, and still applies enough to make me very picky about who I play with now that I have the option to be picky. If options like cons and game stores make you uncomfortable, look at the other options available to you, and see if they are a better fit. With the rise of the internet, a lot of options have opened up. Don't think you're missing out just because you choose other venues than many other players. Focus on the venues that you can play in comfortably and the positive interactions you have with the players you find in those venues. I can say for myself that when I finally did that, my own relationship with the hobby improved immensely.
The internet is really not much of an option. It's just another way to meet strangers who share a similar hobby. I might be okay with getting a new or additional player at a table full of people I already trust off the internet. But, after my experience with the group I met at a game store I'll never join a group without being friends with at least one person in the group ahead of time. For as horrible as my harassment experience was, I was lucky the group's attempt to push me to RP the rape of my character didn't turn into a real-life molestation/rape, and I'll always have that on my mind whenever I meet a group of gamers I don't already know well.