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What you say is certainly true of public school sports and of many private, secular leagues.  Joining a Christian sports league eliminates the Sunday problem, but these are mainly comprised of Protestant schools.  Often, Catholics aren’t welcome because we’re not considered Christians, especially by the type of Protestants with whom we share many moral standards!  Example, Independent Baptists, Holiness congregations, Conservative Pentecostals, and many small, traditionally black and southern state churches have standards of modesty, speech, dress, respect for authority as traditional Catholics.  The problem is that they won’t accept Catholics!  
The Protestants who will accept Catholics are liberal; they accept everyone!  One may as well play public schools and novus ordo schools.
Public school sports was not always as it is now.  When I was in grade six, I tried out for volleyball at a friend’s insistence.  I made the team and she didn’t.  I wasn’t into sports, so my parents were a bit surprised, but I played volleyball for two years and enjoyed it, both games and practices.  There were no Saturday or Sunday activities.  Games and practices were M-F in the afternoon.  We were a middle of the road team, didn’t win the championship, but didn’t lose every game, either.  I didn’t play in grade eight because I chose another extracurricular, the Outdoors Club. When my sister hit grade six, she wanted to try out for field hockey and soccer.  I was already a high school senior, not at all involved in school sports.  My sister made the soccer team and all of a sudden, there were arguments about missing Mass—-never allowed by Dad, and staying over various friends’ houses for the weekend to accommodate Saturday practices and games instead of going camping with the family.  Too often, she got her way with the resulting alienation.  She’d agree to go to Mass, either Saturday vigil or Sunday, but often that didn’t happen.  There’d be excuses, headache, upset stomach, got a flat tire on the bike and it was too late to walk...So then Dad required a Mass bulletin. Well, one needn’t actually attend Mass to get a bulletin!  She had a boyfriend who’d supply one, or she’d pick one up on the way to or from school since the church was a block away.  By grade seven, after screaming, yelling fights, a priest whom Dad consulted said she should not be made to attend church(!?!), so she pretty much left off all religion except the five classes in the evening for Confirmation. Dad and Mom insisted in the hope that it would eventually bring her back.  Sadly, I have serious doubt as to the validity at that point in time.  
Did sports cause the entire disaster?  No, of course not, but it didn’t help, and was definitely used by the devil as one more tool.

The down side of attending a Protestant-led homeschool coop is that they demand that you sign their homemade Creed, not the original Nicene Creed. They also want you to attend their prayer services.

The down side of attending a Protestant-sponsored little league program is that they want you and your child to come early and pray. Sometimes they even have a youth pastor lead prayer services before the game. Ecuмenism raises it ugly head.

What's wrong with boys playing sports?

Absolutely nothing..... especially for the lads.  The problem is playing on an "interfaith sports team" in which religious lines are blurred.  Do they think the evangelical protestants won't try to convert their kids?  They are taught that they MUST under the Great Commission because Catholics are misguided idolaters who are headed to Hell unless they repent of their sins, stop worshiping Mary, and accept a "Fun Jesus" as their Lord and Savior.  We are going to Hell because we don't know that Jesus just wants to be our good buddy, so they have to correct us!!!
Catholic teams playing AGAINST Protestant teams or AGAINST public schools or even playing on non-religious teams (i.e. Little League Baseball) are all fine and build character.  Blurring the lines and letting "Coach / Pastor Bob" influence young Catholics is wrong.  The focus isn't ONLY on the sport, there is the religious piece always just under the surface.  
Will they pray as a team before and after games?  If so, will they hold hands in an ecuмenical and heretical kumbaya or will they say a Hail Mary, invoke the help from Our Lady Queen of Victory, and finish with a sign of the Cross?  Any of you you have ever been around any damn Protestants already know that answer.  They worship a different Jesus than us (a false god):

"Don't worry dudes ,Once Saved - Always Saved, so get out your guitars and drums to play some evangelical rock n roll jams for the kids"

They definitely did their part bleeding us, but to hear it from them they were just willing followers and that they basically did all of the construction / contracting "at cost" out of the goodness of their hearts.  They supposedly made sure that their subcontractors made only meager profits, too!  Come on!  The parking lots and Church steps are cracking all over!  The concrete work obviously wasn't done right (not thick enough and not sealed), but I'll bet the Parish paid for it to be done right!  Costs kept increasing during the course of the project and the donations made for stained glass windows and memorial bricks evaporated into the P&L cost line items covering who knows what expenditures.  Hmm, cutting corners to increase profits as the GC (quality control / cost management duties) while also maintaining the internal auditing powers, wow!  If you play both side you can't lose!  As me ol' granny from Belfast always said, "ay, a snake with 2 tongues makes for double the bite".  I never knew what the ol' gal meant until now!