Remove border lines of SRTM tiles rendered as hillshade

SRTM tiles (3601 px * 3601 px in this case) have 1-pixel overlaps in between. When you apply transparency (or reduced opacity) to your hillshade layer, such overlapping pixels stand out. You may have observed this also on the original images, if you apply transparency (see below).

..... original SRTM, Pseudo-color + 60% opacity

Anyway, you can avoid this by merging these tiles. One way would be Build Virtual Raster (either from menu > Raster > Miscellaneous, or from the Processing Toolbox).

Do not tick on Place each input file into a separate band option.

After setting hillshade on the Virtual Raster Layer, you will not see the boundaries anymore.

As described by @Kazuhito, the tiles should be combined into a virtual raster. Their method is performed within QGIS. If you have a large number of tiles you may prefer to do this from the commandline. To do so open a shell in the directory containing the SRTM tiles and run gdalbuildvrt combined.vrt *.hgt The resulting virtual raster (combined.vrt) can then be loaded into QGIS.