These loose ends are called 'floats' and are the normal result of a shuttle loom.

This type of loom starts with the shuttle, holding one color yarn, on one side. The shuttle is passed through the warp to the other side - and returned to where it began. This creates the true kilt selvage.

When the pattern requires a change in color a second shuttle is introduced with the first place on a shelf of the loom. The second color is then woven and the first is just idle.

Some Tartans with multiple colors will be woven with one shuttle per color.

When the first color is needed again the first shuttle is put back on and continues to weave. The gap between the colors creates long, loose ends. Floats.

This is normal. As this fabric is usually single width only one selvedge is needed. The other long end of the fabric becomes the top where the fabric is cut to the length of the kilt.

So don't worry about removing the floats. You will be cutting the fabric, along with with the floats, away anyway.