I need to update my answer completely. Your problem is not the blur filter. It is working fine. For better improvement for blur you can add
-webkit-backface-visibility: hidden;
-moz-backface-visibility: hidden;
-ms-backface-visibility: hidden;
backface-visibility: hidden;
-webkit-perspective: 1000;
-moz-perspective: 1000;
-ms-perspective: 1000;
perspective: 1000
But the lagg is triggered by the background-attachment: fixed; in mozilla.
Other Prefixes like transform are removing the background-attachment: fixed; completely.
-webkit-transform: translateZ(0);
-moz-transform: translateZ(0);
-ms-transform: translateZ(0);
-o-transform: translateZ(0);
transform: translateZ(0);
I am trying to figure out why
Some Links if you wanna help searching:
Fixed attachment background image flicker/disappear in chrome when coupled with a css transform
The solution of the link above is not working as well^^ not sure why
Maybe you should just go with another solution of parallax.