What can I do to stop my fiberglass bathtub from squeaking?
It's not a great picture, but it looks like the tub is supported by wood and foam.  It's possible that the wood has rotted, or the structure that supports the wood has rotted or been compromised in some way.

You can spray foam under there wildly, if you want. But if the structure that will support the foam (and tub) is compromised, it's not going to do you much good.

You're going to want to get better access, and evaluate the structure.  The answer may be as simple as adding a few extra braces, or as complex as ripping it all out and replacing it.  Without a better look, it's impossible to say for sure.

Since this is a mobile home, it's not likely this is a botched installation. Instead it's likely due to age, wear and tear, and/or rot.