My husband is a LCSW. Recently, he had an Intern with Asperger's. He said he was great! He was able to do exactly as he was told and always had his report ready and very professional. Yes, he did miss social cues; however, once he developed a system and watched my husband, he imitated him very well. A good therapist has to be very scientific too. You'll be good in that way.
About the money, in the beginning it's low, but later it increases. A lot of therapists do private practice twice a week and work for an agency in the day. A few go into administration and still help interns with therapy, like my husband. He loves it. Get your Master's and your license. You also can help small agencies that do not have a licensed social worker. It's easy and extra money. My husband does that, and he does adoptions once in a while. Those assessments are long but run from $1000 to $2000 a family.
A supervisor makes over 80,000 a year if you've been in an agency for some time.
I say go for it! Try it out. You will be accepted in the field since everyone that goes into Social Work knows they have some kind of dysfunction. Everyone in my husband's office knew the intern had Asperger's without him revealing it. No one said anything, they just adapted to him right away, treated him very professionally and helped him with his weaknesses while focusing on his strengths.