In September, IEX Group Inc. threw a party at Manhattan’s Bowery Hotel to celebrate becoming a full-fledged stock exchange.

The party had guests from high-speed trading firms such as Citadel Securities LLC, Global Trading Systems LLC, IMC Financial Markets and KCG Holdings Inc., people familiar with the situation said. They came even though IEX vaulted to fame by crusading against ultrafast traders who use computers to exploit slower investors.

IEX...