I still don't see how "rhythmic gymnastics" and synchronized swimming are in the Olympics, but REAL sports like baseball aren't.
I hope you're kidding and/or trolling with the "real sports" jab.
Either way, multiple factors. The sport's not popular in Europe, where IOC holds a strong influence. MLB is not willing to stop their season so the top players play like the NHL does. Softball being totally dominated by the US. I'm sure organisers don't like getting stuck with purpose-built baseball/softball stadiums they'll never use after the Olympics end.
They can use soccer stadiums for baseball, just like football stadiums do (see the Raiders and Athletics). And baseball is a sport, rythmic gymnastics is mostly just twirling a ribbon, and synchronized swimming is not even close to a sport. There is a strong anti-American bias in the IOC. And so what if MLB will only let minor league baseball players participate? Some of the more popular Olympic sports use amatuer players (like boxing and skating). Plus, the fact that baseball is becoming even more popular in Japan (which is hosting the 2020 games), increases its chances of being brought back. Besides, rugby is now in the Olympics and that is popular is a handful of countries (mainly South Africa, Australia, and New Zealand).
I am glad Nintendo and Sega are continuing these