I've never considered fingerprints to be a massive problem in a "I drive a family wagon to the shops" context but if this is on your Porsche just before tomorrow's track day you might feel differently. That many rotors come with a film of oil to prevent corrosion is slightly more significant, and that should be thoroughly cleaned off.
Safety purists will likely advocate that all grease and contamination should be removed but in real life terms driving through a puddle contaminated with oil/ diesel is likely to splash your brakes with an equivalent amount of oily contaminants - the volume of grease deposited by fingers will be low because you can't work with fingers laden with large gobs of grease; most of it will be on the rag. In addition to this, the temperature that well-used brakes run at will tend to reduce oily contaminants over time, but don't be tempted to go out and deliberately cook new brakes just to try and remove a minor amount of oil as overheating new pads will do more long term damage
Only you can judge whether you feel your braking system is now deficient. It's normal for new brake pads and rotors to feel less grippy than the old ones, because the friction surfaces haven't had time to wear and bed together to form a large contact area, but after a few hundred miles they will have
Tip for future changes, if you didn't do it this time; open the bleed nipple on the brake calliper before you push the piston in, and drain the fluid as you retract the piston; doing this routinely reduces the amount of time brake fluid stays in the system, helping with the regular change needed. Fluid in the callipers is the most likely to be contaminated and is best expelled rather than pushed back into the rest of the system