The derivative of StereoCamera.project:

H1=(1/z)(({{fx, 0, -fx xL/z}, {fx, 0, -fx xR/z}, {0, fy, -fy y/z}})).(({{0, -z, y, -1, 0, 0, R00, R10, R20}, {z, 0, -x, 0, -1, 0, R01, R11, R21}, {-y, x, 0, 0, 0, -1, R02, R12, R22}}))//FullSimplify//MatrixForm

To get rid of (1/z) factors, work in terms of u=x/z and v=x/z.

H2=H1/.{xL->z uL/fx,xR->z uR/fx,y->z v/fy}//FullSimplify //MatrixForm

Finally, avoid divides, version one, with annoying (but efficient) non-physical v1 and dx:

FullSimplify[H2/.{1/z->d, v -> v1 fy},{z d ==1,v1 fy ==v,  fx v1 == v2, d x ==dx}]

Second version, with u and v not divided by focal lengths (i.e., intrinsic coordinates):

H2=H1/.{xL->z uL,xR->z uR,y->z v}//FullSimplify //MatrixForm

FullSimplify[H2/.{1/z->d, x-> uL/ d },{z d ==1}]