It's worth noting up top that strength of schedule is not that important a factor in the MLB season. This isn't football, where teams play a very unbalanced schedule, face only a fraction of the possible opponents and the omnipresent specter of traumatic brain injury.
Over 162 games, the strength of everyone's schedule comes close to evening out. But there are still variations. Jeff Sullivan looked at the projected strengths of schedule based on average opponent WAR (and not other factors like home/road), and found a difference of about 1.5 win between the strongest and weakest. That's not huge, but it's not nothing, either.
Sullivan projects the Cardinals to be tied for the third-easiest schedule in the NL, behind the Nationals and Dodgers, tied with the Marlins. As he notes, good teams tend to have "easy" schedules simply by virtue of not having to play themselves.
But while things even out over the full season, there are still strikes and gutters, ups and downs within the season itself - strings of tough opponents, brutal road trips, etc. For that reason, let's look at the Cardinals schedule on a month-by-month basis:
10 Home; 12 Away
Opponents Above/Below .500: 6/16
To calculate opponents above/below .500, I'm simply looking at the Fangraphs projected standings and counting up those above and below that line. Opponent-wise, April projects as one of the softest months of the season, with only the current series against the Cubs and an away series at the Nationals against teams projected to be better than average.
16 Home; 13 Away
Opponents Above/Below .500: 23/6
After a relatively soft May, the Cardinals face their strongest slate of opponents in May, including tough road series against the Indians and Pirates, as well as the Dodgers at home. Most project Pittsburgh to be the Redbird's toughest opponent in the division, and they will meet six times in May.
12 Home; 15 Away
Opponents Above/Below .500: 7/20
Aside from a road trip to Los Angeles, June looks relatively easy, including series against the projected worst team in both leagues, the Phillies and Twins, respectively. Or maybe without respect. Those teams look like garbage.
16 Home; 9 Away
Opponents Above/Below .500: 14/11
July is divided neatly in half not just by the All-Star break, but by a clear separation in terms of the quality of opponents. The tough teams and most of the road games are in the first half of the month, while the second half of July includes home series against the Braves, Reds and Rockies.
12 Home; 16 Away
Opponents Above/Below .500: 13/15
The Cardinals play the most games on the road in August, including their longest road trip of the season - a West Coast swing that has them play ten games in ten days.
15 Home; 13 Away
Opponents Above/Below .500: 14/14
While the Cardinals make another 10-game road trip in September, they still play more of their games at home for the month. Aside from the tail-end of a series against the Nationals to start the month, the Cardinals only face teams within the division.
0 Home; 3 Away
Opponents Above/Below .500: 0/3
While it would be best to end at home, a three-game series against the tanking Braves is a nice prospect in the event the Cardinals need wins in the final days of the season. If you're trying to win as many games as possible, it's great to play a team that's trying to lose as many games as possible.