Serve any extra dressing with wedges of Bibb lettuce.
Preheat oven to 375 degrees. Place English muffins on a rimmed baking sheet, brush with oil, and generously season with salt and pepper. Toast in oven until golden but still slightly soft in centers, 16 to 18 minutes. When cool enough to handle, tear into bite-size pieces. Meanwhile, whisk together mayonnaise, scallions, and vinegar. Season with salt and pepper.
Remove stems and center ribs from chard with a knife and set aside. Stack a few leaves at a time, roll up like a cigar, and thinly slice crosswise; transfer to a large bowl. Cut chard stems and ribs crosswise into 2-inch pieces, thinly slice lengthwise, and add to bowl with chard. Chard can be prepared up to 1 day ahead, covered with damp paper towels, and stored in refrigerator. Just before serving, toss chard with croutons and cantaloupe; garnish with scallion tops. Serve with dressing.