How to filter objects on basis of orientation of regionprops
I don't have MATLAB, but here are a few ideas:

Since you use regionprops, you could use the Orientation parameter - which is pretty much exactly what you want to have.

Another idea


Create an matrix of the same size as your image. The matrix has entries that give a linear variation in the perpendicular orientation that you desire (it basically is a gradient field in the perpendicular orientation, e.g. with values ranging from 0 to 1).
Use bwlabel to label all your candidate lines
Loop over all labels and create a binary mask for each label. Multiply the mask with the gradient matrix.
Calculate the variance inside the mask. Since the gradient is perpendicular to your direction, the variance should be 0 for a perfect line. For a not-so-perfect-line, there is a certain variation. You could use


an empirical threshold 
check the math for an more elaborate threshold, because one can certainly find a function $\sigma^2(\alpha)$, with $\alpha$ being the angle of the region of interest in the mask.