Rather than sue MLB for moving the All-Star game and related activities, this business group would've been better served by spending that money and effort to implore their lawmakers to not enact the legislation that caused MLB to make such a move to begin with. The MLB was well within its right to move the game and related events to a state they felt was more reflective of their values and those of their owners, players and/or fan base.
This is somewhat similar to a situation a few years ago when North Carolina passed the controversial "bathroom bill" which was seen by many as targeting the LGBTQ+ community. After the NBA and NCAA cancelled major events in that state, a number of major concerts and shows were also cancelled and companies like PayPal and Deutsche Bank cancelled expansion plans into that state, it became apparent that by passing this bathroom bill, the conservatives that voted for it had more or less directly cost the state upwards of $4 billion. They ultimately made the decision to repeal it.