I have a 1989 Mazda 323 2WD hatchback that needs new struts, front and back. I also have the official shop manual. The manual does not mention using a spring compressor during strut replacement. The manual says, in summary, to get both wheels off the ground and remove some bolts. The manual only shows using a spring compressor to remove the spring, not to replace the struts.
Does that mean you can replace Mazda 323 struts without using a spring compressor?
I don't know about your car in particular, but on a lot of Japanese cars of that age, certainly the rear struts don't pass through the springs. Replacement of the rear struts is therefore possible without removing the springs.
At the front end they probably use Macpherson struts. The whole strut, including the top mount is normally unbolted and taken out, then the strip down begins. You will need a spring compressor to remove the springs from the old struts and install them onto the new struts.