Will changing exhaust on a 2.3 L ecoboost mustang mess up the computer of the car?

a V8 will sound like a V8 and a turbo 4 cylinder will sound like turbo 4 no matter how you configure the pipes. as for computer you will need the computer adjusted for and changes like fuel, spark and EGR you can buy those SCT tuners but sometimes the owners want to go full send too fast and you will want to keep the original cat back exhaust in case you sell the car or want to revert the car back to standard configuration.

If you instal a cat-back system,the exhaust back pressure will be reduced which will cause the turbo to cut in only at a higher rpm and the EGR valve will show insufficient flow tripping the CEL light. 

" and I want it to sound...well like a mustang."

It's definitely not going to sound like rumbling throaty V8, if that's what you're envisioning. You're not going to get that classic muscle car sound. 

"But I’ve heard since it’s ecoboost it cannot have an after market exhaust because it will throw the computer off."

Total bullshit. Assuming it's a catback system, the computer has no idea what is happening past the downstream O2 sensor (sensor right after the cat). It's not going to matter.

"What are my options? "

You can get a catback exhaust if you want to. But it be aware of what it's actually going to sound like vs. what you think it's going to sound like. Also the turbocharger also acts as sort of small muffler by itself as it's driven by the exhaust. It makes a small, but noticeable difference in the sound as well. 

First of all there is no way to make a turbo charged engine sound like a normally aspirated engine. If you want your mustang to sound like a V8 mustang- then buy a V8 mustang. It will be cheaper in the long run then spending money trying to do the impossible. There is one other way around it and that is to get a sound generator that ties into the throttle pedal to get the V8 sound.

Me, I don't mind others hearing my turbo charged 4 cylinder.

The car can have an after market exhaust fitted with out messing up the computer. It is called a "Cat-back" system. Such a system replaces only the exhaust system after the last O2 sensor. But no after market exhaust system can produce the normally aspirated V8 engine sound.

It should NOT affect it if you retain the O2 sensors! GOOD LUCK!

There are tons of cat back exhaust systems for your car.  Go to a muffler shop.  Bring buckets of money.

As long as you leave the catalytic converter and O2 sensors in place it will be fine. Know that it is illegal to remove the converter and the engine will not run correctly with it removed. 

It will NEVER sound like a mustang - it is an I-4 the best  sound that you can hope for is a nagasaki nut-bucket with an aftermarket fart can. 

Save the money for your next car and buy what you really want.....A V-8.