My favorite quote about the Red Stockings comes from William Ryczek's Blackguards And Red Stockings where he writes that "(the) Reds of St. Louis were alive only in that they had not officially disbanded." It's a beautiful, cutting turn of phrase but it's only accurate within the context of Ryczek's book and the 1875 NA season.
Ryczek is rather dismissive of the Reds and, again within the context of his book, I think that's fair. But the Reds had been a successful St. Louis amateur baseball club before joining the NA and, after dropping out of the Association, continued on as a prominent St. Louis baseball club.
If you read the contemporary newspapers of the day, the Reds prominent position in the St. Louis sporting scene is clear. I don't think that there is any doubt that the Globe-Democrat was a "Reds" newspaper and took a very pro-Reds stance when it came to the rivalry between the Reds and the Brown Stockings. The Globe, while taking every opportunity to praise the Reds, goes so far as to denigrate the Browns, referring to them in 1875 as a "professional, eastern, atlantic" team. That's rather harsh criticism given St. Louis' position at the time as one of the last bastions of amateur baseball, especially when they were constantly referring to the Reds as "our boys".
After July 4, 1875, when the Reds played their last NA game, "our boys" may have been dead to the Association, Ryczek, and baseball history but they soldiered on. The Reds continued their 1875 season, playing games until November. They had plans to once again compete for the whip pennant in 1876 but William Hulbert and the "big" clubs kind of put the kibosh on that. They were instrumental in the formation of the International Association in 1877 and they continued on as a baseball club until playing their final game on July 7, 1886.
In the intrests of full disclosure, I will state that I am biased when it comes to the Reds. They are my favorite team in the entire history of baseball. The 1875 team fascinates me. Here's a team from one of the great hotbeds of baseball with an original member of the '69 Cincinnati Red Stockings running the show, one of the great catchers of the 19th century behind the plate, possibly the first Native American ballplayer in big league history in right field, and a notorious cheater and hippodromer on the mound. They have nothing but a season full of drama and chaos. The managers bring in Charlie Sweasy at the last minute to captain a club full of the best amateur players in St. Louis. There's the built in rivalry with the Browns that turns bitter very quickly. There's the horrendous weather in St. Louis at the beginning of the season that just crushes their attendance. There's the classic 1-0 loss to the White Stockings. There's conflict with the Eastern teams over scheduling. There's money problems. Their pitcher gets tossed off the team for throwing games. And half the players bolt for other teams in July. What's not to love about this story.