What effect does a direct crosswind have on takeoff performance?
The effects of a constant crosswind up to the demonstrated value are insignificant (at least for airliners), as ymb1's answer already says. I checked some Boeing FCOMs and crosswind is never mentioned for takeoff performance calculation. It can therefore not have a significant impact. Boeing recommends this technique:

Any deviation from the centerline
during thrust application should be countered with immediate smooth and positive
control inputs. Smooth rudder control inputs combined with small control wheel
inputs result in a normal takeoff with no overcontrolling. [...]
Note: Excessive control wheel displacement during rotation and liftoff increases
spoiler deployment. As spoiler deployment increases, drag increases and
lift is reduced which results in reduced tail clearance, a longer takeoff roll,
and slower airplane acceleration.
[emphasis mine]

A gusty crosswind may however require larger control wheel inputs, which result in spoiler deployment. This will impact takeoff performance. Boeing therefore recommends to use more than the minimum required thrust in these situations:

For takeoff in gusty or strong crosswind conditions, use of a higher thrust setting
than the minimum required is recommended. When the prevailing wind is at or
near 90° to the runway, the possibility of wind shifts resulting in gusty tailwind
components during rotation or liftoff increases. During this condition, consider the
use of thrust settings close to or at maximum takeoff thrust.


Source: Boeing 737 NG FCTM 3.15 - Takeoff and Initial Climb - Crosswind Takeoff