When it is resized, it is no longer in the same parameters, and PS/your graphics card has to "figure out" what might be closest. What you should do is finish the image WITHOUT scanlines, resize it to the finished size to be presented/animated/shown/printed/whatever, and THEN apply the scanlines.

When it is a matter of the BROWSER having to resize something with a dense pattern, it will not be an even resize, and you will get the moire pattern. This is then the problem with your graphics card - not a bug, or a bad piece of equipment, but simple math for visual representation that doesn't match dimensions.

To see what I'm talking about more blatantly, make a 512x512 image in PS and apply the scanlines. When you view this at 100% it is perfect.

Hit Ctrl+Minus Key to zoom out, and it will zoom out (which will land at 66%) and it will have the moire pattern, do it again (which will display your image at 50%) and it will be perfect again. Do it again (now 33%) - moire pattern. Do it again (now displaying 25%) and it will be perfect.

In increments of 25% it will display correctly - ANYTHING ELSE and you will get the moire pattern. Your browser doesn't care - it is merely resizing so you are able to see all of the image, regardless of percentage.

End solution, size the photo to be the correct size in the finished product and NOT be resized by the browser, and THEN apply the scanlines.

Hope that helps - good luck-
-Lew ;-)