Can I use any 2-cycle oil in my 2 cycle engine?

No.

I know, you're going to tell me that you've been using your marine 2-cycle oil in everything from your ATV to your Weedwacker and haven't had a problem. At least yet anyway.

There are many new requirements that manufacturers are putting in place for their modern engines. Take for instance the Rotax E-Tec 800R snowmobile engine. In an effort to reduce emissions less oil is injected into the engine, but the engine is capable of 163.9 HP at 7,900 RPM. So even though less oil is used, it doesn't mean that less lubrication is needed. In this case the manufacturer states that you must use their own oil and nothing else will work. That's not entirely true. Amsoil has oil that will work in that case, and in fact, in a study, using Amsoil showed less wear on the piston and piston wall than using the manufacturers oil. If you'd like more information on that study let me know and I can provide you all the details.

So, yes, you need to use the correct oil for your application, but the correct oil isn't always what the manufacturer claims. Do your own research and look for the oil properties that the manufacturer requires and then find the oil that works best for that application. To help you find the oil that works best for your application follow this link:
https://www.amsoil.com/whymygarage.aspx?zo=1864485