Your OCD doesn't have to be exclusive to only Pure-O or ritual-OCD. You can have bits of both, more of one than the other, it's a continuum not a black/white scenario.
Sexual obsessions (pedophile fears, homosexual fears), religious, murder, and harm obsessions all fall into the Pure-O category because they are all mental ruminations. You couldn't tell the person is going through it because there are no visual compulsions. The debate is all in the mind.
Hand-washing, lock-checking, going through doors multiple times, not stepping on cracks, arranging things, etc etc is typically known as ritual-OCD. Because it is more visible to others, and sufferers are more willing to discuss ritual-O than Pure-O obsessions, it is stereotyped as the most common OCD. When people with very little knowledge of OCD think about it, they think about hand-washers, counters, lock-checkers yada yada... not pure-Os.
The one constant with all types and subtypes of OCD is your basic insecurity or paranoia.