And while the game was different back then, a win is still a win. And these aren't the All-Century teams, they're the ALL-TIME Teams. And the players are picked based on how many wins they helped their team rack up, regardless of when that was. Now to be sure, hitters don't really get that much of an advantage. Most of the 1800's hitters that made their teams are either in the Hall of Fame or guys that you would otherwise expect to see. Pitchers... that's a different story.
1800's pitchers do have a slight advantage (or at least a difference) when it comes to WAR, assuming they were any good at all in the first place. WAR for pitchers is heavily dependent on Innings Pitched. And those guys would regularly make over 50+ Starts a year, pitching 450 (or more) Innings doing so. That's basically double the workload of a modern pitcher. So they could rack up WAR pretty fast. On the other hand... all that extra workload meant that most of these guys had very, VERY short careers. A lot of these 1800's Pitchers got most, or all, of their WAR in just 2 or 3 seasons. Of course, these were equivalent workload of 5 or 6 modern seasons, so it still kind of evens out: They had higher peaks, but shorter careers. And if those seasons really were that good, then why shouldn't we recognize that?
Really, the biggest problem with modern players making these teams is that so few spend enough time with one team to build up their Career WAR numbers with that team. Small market players leave too soon for bigger markets, while a lot of those big market teams have been around for awhile, and have built up a pretty hefty roster of players over those years. A guy might spend 10 years with the Yankees, but good luck trying to break into THAT Outfield! (Just ask Hall of Famer Dave Winfield, of the All-Time PADRES, how that worked out!) All the same, most teams will still have an active player or two on them. There's no rule against it, provided they have the WAR to rank.
Pitctured (clockwise from top-left): Who (1B), What (2B), I Don't Know (3B), Why (LF), Because (CF), Tomorrow (P), Today (C), I Don't Give a Darn (SS) and Nobody (RF)