Is it bad to learn more than one instrument at the same time? I get it, learning and experimenting with new instruments can be a lot of fun! However, I would caution you against learning too many instruments at once. Let’s talk about some different scenarios you might find yourself in.
You are starting an instrument: If you are just starting an instrument for the first time, this is not the best time to learn more than one instrument. It can get confusing to switch between instruments and in some cases, it can hurt your technique especially when the two instruments are similar in the way they are played (two brass or wind instruments, two string instruments, etc). Also, you need to put in enough time on one instrument to become better and to learn that instrument. If you spread yourself too thin, you won’t be able to improve on any of the instruments.
You have played an instrument for years and want to pick up a new one: This scenario is a little different. If you have played an instrument for a long time and want to pick up a new one, you might be ready to do so. I would highly recommend having the basics of you instrument down before adding another to the mix. You want to know how to create a good sound on the first instrument and should be able to play all the notes easily. These prerequisites of course will differ from instrument to instrument.
You want to play multiple instruments in the same family: Especially in the wind and brass family, you might find yourself in a situation where you want to explore another instrument in your instrument family such as a piccolo if you’re a flute player or an English horn if you are an oboe player. This is common but, again, it’s important that you have a very good grasp of the basics of your first instrument before playing these “auxiliary” instruments. If you move to these too quickly, it will mess with your fundamentals.