I just took a gander at the MLS and MLB playoff schedules. There isn't a scenario in which either Yankee Stadium or Citi Field would be available for the first round - at least not with enough notice to plan a game there.
The Yankees will certainly win their division and end up directly in the divisional playoffs as host. That leaves them in line to host games the same weekend as the MLS first round.
The Mets are likely in the same position, and if they win their division Citi will be booked. They have a 2-game lead on the Braves, but even if Atlanta manages to pip them and take the division, the MLB playoff schedule leaves too much uncertainty to plan for a soccer window. In that scenario, Citi Field would host a game on Friday, too close for an MLS game on Saturday or Sunday. Plus, if they win the Divisional Series, they could end up hosting a playoff game on Tuesday, meaning the Monday date might not be open either.
Yes, the Mets might lose in the wild card or Divisional Series or be the road team in the LCS, but none of that will be known in time to commit to a game at Citi Field.