I've seen the Jays in a handful of opposing ballparks, so here's my experiences in each one:
Boston: I saw the Jays there on 3 occasions between 2013-2014 and never really had any issues. The first game was Wang's bad outing in June 2013 when the Jays got shelled, but the latter two were Jays wins. The only real "issue" I had was someone yelling at me (I can't even remember what, but I just ignored it) after Melky Cabrera homered in the top of the first inning. Jose Bautista homered in the next at-bat and no one said anything to me after that. Plus there were a lot of Jays fans there, so it's not like I was 1 among 35,000 Red Sox fans.
Baltimore: I saw the Jays here in 2011. It was a small crowd (Brian Matusz bobbleheads were supposed to be given out to the first 20,000 fans and only 19,000 fans showed up). I had no problems at all, and in fact the staff in the ballpark were very friendly to my girlfriend and myself since we were out of towners.
New York: I saw the Jays at Yankee Stadium in 2012 and 2014. Surprisingly I had no issues, but I also was in the upper deck sitting among a bunch of tourists and non-Yankees fans.
Cleveland: I saw the Jays here in 2011 and 2015 without any problems at all. 2016 at the ALCS, however, I did have one douchebag couple saying things to me unprovoked for a while. After the game, the woman made a crying gesture at me and finally I'd had enough so I went over to ask her what her problem was. She pretty much just sarcastically told me to have a nice ride home and then her husband came over to defend her and he more or less told me the same thing. I shook his hand and said "you too, **********" and at that point he decided to get out of there immediately as he kept looking over his shoulder at me on his way out. After that though, a nice couple in their late 40s came over and chatted with me for about 5 minutes, so I had a pretty good experience overall in Cleveland.
Detroit: Saw the Jays here in 2010. No problems that I can recall, other than some cute girl playfully talking junk to me as the Jays were winning. One guy behind me told me to sit down after I applauded Jose Molina's home run. I was about to tell him to "f*** off" until I remembered I was there with my parents
Pittsburgh: Saw the Jays here in 2008. No problems, but then again it was about 1/3 Jays fans, so....
I think that covers it.