You think Peter Parker and Steve Rogers ever discussed baseball during that time Peter, MJ, and Aunt May were living in Avengers/Stark Tower?
I guess it could have happened some other time, but once you get past that stretch, you have the period where Steve was "dead", then there's the stretch where Otto had Peter's body, and you figure there wouldn't be much time during the non-stop barrage of big events that took place in-between those things. But they had downtime at the Tower. It was a Bendis written team book, what else would they do but shoot the breeze? Certainly not fight evil.
Lazy old jokes aside, Paul Jenkins, at the very least, established that Peter and Uncle Ben used to go to the Mets' season opener every year (what, like Parker was gonna be a Yankees' fan? Please), and that Peter had continued the tradition by himself. Why not? Plenty of nerdy folk like baseball. I read quite a lot of their writing about it online (I may also be one, depending on whether I'm smart enough to qualify).
Of course Steve Rogers likes baseball. He grew up in the 1930s, and I can't see him gravitating to horse racing or boxing, which were the other two major sports at the time, I think (professional sports, anyway, what with college football being "amateur"). I'm fairly sure it's established he was a Brooklyn Dodgers fan, but regardless of when the sliding timeline says Steve was unfrozen now, the Dodgers had long since moved to the West Coast by then. Which wouldn't preclude him from continuing to root for them (though my father abandoned the now-Arizona Cardinals when they left St. Louis), but I think Mark Waid had Steve adopt the Mets as his team. Again, makes sense. Like Captain America is gonna root for the Damn Yankees.
There was an issue of "The Other" story arc, early on, that showed Steve and MJ shooting pool. MJ was kicking Steve's butt, which I love, and mimicking some move Tom Cruise did in Color of Money because she thought it looked cool, which seems appropriate for MJ, but eh, Tom Cruise. Anyway, I mostly mention it because I like Steve Rogers just casually hanging out with people.
I have this impression that a lot of people tend to get stiff and formal around him because it's CAPTAIN AMERICA, and Steve would rather people just relax, so he works to make a connection. It probably wasn't much of an issue with MJ, she's generally a friendly person, seems to get along well with people that are worth getting along with (read: not jerks), but you know Peter would be on edge around him. So Steve would want to find some non-costume related common ground, and baseball might be one. I'm not sure either guy would want to talk about their history of getting picked on, or losing parents at a young age. Steve's an artist, Peter's a scientist, though maybe Steve could comment on the composition of some of Peter's photographs. Anyway, baseball wouldn't be a bad ice-breaker. If Steve did adopt the Mets as his new team, Peter could give him a live perspective on some of the things he missed.