The Royal Society is important because it is where the UK government go when they need good advice on scientific issues. Many people in the US might think that their government doesn't need good advice on scientific issues but, as they will find out, they are wrong.

If so, why would one automatically assume Musk has the bad advice and the rest of them have good advice? It's awfully ironic as science is literally the process of demonstrating the widely-accepted wisdom (preeminent theory) wrong.

Do you want to take a risk of going down the history as the society who estranged Galileo? Even the haters secretly know that the likelihood of Musk being remembered in history books is higher than a random FRS. In fact, that's likely why they are jealous and eager to write such letters.