It looks like the MLS season will resume, but in an altered format. The schedule is to continue in the form of a tournament to be held in Orlando and subject to team testing protocols.
From the MLS website:
Plan set for MLS return to full team training with testing ahead of season restart
MLS, Players reach new agreement, sets stage for resuming 2020 season
Details to be provided in the coming days. In addition to the tournament, there is a plan to finish the season with 20 games scheduled, with the probability of those matches being played behind closed doors. As of now, the Quakes are the only team that has not resumed training. The NPSL and USL League 2 seasons have been cancelled, while NISA is planning to resume in the fall. Right now, only two players have tested positive for Covid-19 so expect a routine amount of testing leading up and during the rescheduled games.