As discussed in another question, some people have lower back pain during straight leg raises. Why? Many places on the internet will tell you that these people have weak abdominal muscles, and they can't control the tilt of their pelvis. That is probably true. However, there must be more. I would guess that there is a disk bulge which, together with weak abdominals, is creating the pain. On the other hand, the pain happens when the lumbar spine is extended, and that is not when a posterior disk bulge would be pushing into the spinal cord. Can anyone help me figure this out?
It's helpful to take a look at the anatomy of your psoas major muscle, which will be heavily recruited during straight leg raises. You can see that it attaches to the lumbar vertebrae, the result being a compression of your lumbar spine when it is under tension. So even if you can maintain a neutral spine position the compression could still result in pain if you have a bulging disc.
You allude to the other possible issue of people being unable to control their pelvic tilt when performing this exercise, this results in the lumbar spine going into extreme extension and potentially irritating the facet joints.
Why don't you try it yourself and be aware of your lower back and abdominal muscles while doing the mentioned exercise. This way you will get a strategy instead of only an answer.