No - if the cylinder is infinitely long we never get closer to one end than the other. There is no reason for E to tilt to one side of the other. E does vary - we get closer or farther from the cylinders, so there is no symmetry here. Calculate the total flux through the closed surface and apply Gauss' Law. E is constant since sides are at fixed distance r .
E is parallel to the area vector since both are in the radial direction.
The flux is since E is constant it can come out of the integral. Apply Gauss' Law Total Flux through Gaussian surface Charge enclosed in Gaussian surface Calculate E for The only flux is through the sides, where E is constant at a fixed radius r.