Many of the answers provide purely inspirational answers, which have value. Children are our future! However, there is a reality that we selfishly expect more out of our life than to be slaves to our children. I mean really!
So you have a balance of desires. The child is passionate about music, but you are not confident the world will be kind to their musical skills. You want the child to be happy in the long run (potentially longer than they are even aware of at age 9... not many really understand what it means to hold a musician's job!). And then there's the short term issue of the racket.
The short term part has the easy solution, as mentioned, of getting the kid to prefer an electric instrument, with headphones. However, that still doesn't resolve the long term issue of letting a child go down the wrong path.
But is it the wrong path? If there was ever a way to tell the right path from the wrong path, I'm sure it'd appear in a parenting book. Judging by the scathing reviews on Amazon, no parenting book has this magic tip in it yet, so I'm assuming no one has written a way. I don't expect to either. You'll have to find your own solution.
However, there is a reasonable solution which you can fall back on if you haven't figured out any better solution: a dose of reality... for both of you. Let's just focus on the long term bits (you can suck up the short term issue of cleaning up lizards off the floor, or convince them to do the electric instruments). Your positions are different enough that they're not polar opposites... just really really far apart:
- The child is passionate about music, and wants to continue further. Arguably the child wants to spend their life doing music (even if their concept of what that means is a bit shortsighted at the ripe age of 9)
- You believe you understand what music is good and what is bad, and you believe the child will be unhappy in the future because the world will not appreciate their music, and the child will have spent their formative years "wasting" their time on that dad-gum instrument!
The best solution is to find a win-win, so that the child can continue being passionate. You really don't want to snuff that out. Failing to do so, you can always fall back on testing both of your positions. Convince the child that, if they want to continue down the musician path, they should experience more of the reality that they are entering (you know, that reality we always shelter our children from!). The child needs to pony up, and test their desire of musicianhood against their actual abilities. Find a way to build a game where they have to use their musical skills to "make a living." This could be as literal as throwing the kid on a street-corner to play their instrument for tips, or it could be a more intellectual game. Perhaps you think their sense of tempo is obnoxious. Build an objective game where they are rewarded for playing in tempo (perhaps as literally as "you can use the amplifier rather than the headphones for 2 minutes for every tempo exercise that you pass"). Let them have to work for their passion, and see if music really is their passion.
This is where the key is. If music really is their passion, it won't matter a lick of difference to them whether others like their work or not. They'll live the life on a street corner, playing for tips, absolutely content that they actually got to live the life they wanted to live (how many get the privilege to claim that!). If it turns out that they value other things more, they'll learn that maybe music isn't really their passion, and you can sigh with relief at the blessed silence.
And if you do your job really well as parents, you'll find a way to dislodge a child's misguided passion for music without killing their passion in the process. It's really quite a skill, dislodging a passion without killing the underlying passion that drives the person. Most of us are really bad at it. We could kill the passion in a lizard as we try to convince it that it's really bad at climbing walls!
On that topic, how passionate are you about being parents? These sorts of "put your money where your mouth is" arguments also work for bettering ourselves, if we decide they are rational enough to give them a shot (feel free to argue they're not rational! I don't mind!). You could challenge yourself to really pony up and try to show your passion for parenting. Develop games like "deal with 30 minutes of ear splitting racket to earn unlimited access to the bottle of wine/beer after 9:00." Along the way, you just might accidentally figure something out to help you work with your child on their passions. You never know. As always, use your own judgement in your own life; I'm just an anonymous voice on the internet. What do I know about you?
Lizards off the wall? Really? I bet that could make a killer reality TV show!