I'm one of those people who can't stand a picture that's crooked on a wall, so something "off" in one of my quilts drives me crazy.
I've been quilting for 44 years so I've learned a lot. One of the things I had to accept is that perfect intersections aren't easy, particularly by machine and when cut to template size.
Accuracy is hard to achieve when you are working within very tight parameters. 1/4" seams leave very little room for error. So years ago I started adding an additional quarter inch to my templates. I still sew the 1/4" seam, then I trim to the correct size. I use a gridded ruler to make sure everything is square. When my pieced sections are squared I baste a stitch or two at intersections before sewing. Then I stitch them together with 1/4" seams, and check for square again. I always make extra pieces so if something is off I have another piece to use.
This takes extra time but is the only way I've found that works well consistently. It took a lot of years to figure this out so if you're still struggling keep trying and you'll get there. It takes a lot of patience to get it right but taking the extra time does pay off.