If employee has OCD, can he be exempt from being written up/fired if he refuses to do certain tasks because he’s busy straightening things?

he or she should perform the daily task and then some...  and then If he's wiping off the counter just let him...

No, he is definitely not untouchable. All jobs depend on being able to do them--and if this person can't do the job he was hired for, then he can be fired. A disability depends on a medical diagnosis to be exempt. Just because you THINK someone has OCD or Asperger's, that's not considered being disabled. And any disabled person who cannot do the job they were hired for is fire-able as well. It isn't something that will keep a person from being let go if they simply cannot do the job they were hired into. 

It's sympathetic to try to understand that the person is hampered by the condition they have--if they truly have that condition--BUT--it's not practical. A supervisor wants an employee that can do the job--no matter what conditions they have. And if that person cannot do it, then they either don't get hired, or they get let go. 

If they don't know you have a disability, you can easily be fired. You don't say what kind of job this is, but most states can fire for any non-discriminatory or no reason. i am not sure if this would be a firable offense for all jobs.

Sounds like you are asking to be fired.  Do what you are told to do, when you are told to do it.  You're not the boss.

No he's not exempt.   He works at a place of business,  he needs to do the duties of the job.

Nope, not untouchable. Incidentally, if he has a condition covered under the ADA, you would not be aware of it unless you are HR or his immediate supervisor. He may have reasonable accommodations made for him due to his disability. 

If you are the employee, you are not untouchable. If you are not the employee, you need to stop spamming stuff about this other person and the issues you have in working with him. 

You can be fired for any reason. You’re hired to do a specific job, not straighten things that don’t need straightening. Regardless of the reason, if you aren’t up to doing the job you were hired for, then they’ll fire you and find someone who will do the jobs they’re asked to do.