My son melts down a lot around strangers; any advice to help him get over it?

Posting this for my wife who has been having issues with our son (20 months) when she tries to take him to any of the classes she signed him up for - swim class, little gym.

Little bit of background, or sun stays home with me, the father, on Mondays and Fridays when I can work from home his mother on Tuesdays and Thursdays when she is off and his grandparents on Wednesday. He hasn’t started daycare and my wife doesn’t want to put him in daycare until he’s around two.

She signed him up for a little gym a while back and classes were going well but recently he started throwing a fit at the beginning of the class and it takes him about half of the class to calm down before he even wants to participate. Same goes with his new swim class. He’s fine when he gets there and then when he has to interact with the instructor or the group he has a complete meltdown and my wife is getting really frustrated with it. She says it takes her about 20 to 30 minutes every time to get him to calm down and get in the pool with her and once he’s done he actually does a lot of what he supposed to.

We really want him to interact with other kids and he does well in our neighborhood with all of the children that live on our block, which is a lot. We also want him to learn how to swim because his grandparents have a swimming pool in the backyard, I suggested private lessons but I also want him to get over his fear of working with others in a public setting so it’s kind of a win/lose there.

Not sure if there’s an immediate solution but looking for some advice to maybe help ease him into it better than what we are trying currently.