Yes you can wash stuffed animals such as plush toys in the dishwasher and use some regular laundry detergent.
However if you have a front load washing machine or a washing machine without an agitator then you can safely wash the stuffed animals and other plush toys in the washing machine on the gentle cycle.
If you washing machine has an agitator then I would not wash stuffed animals in the washing machine because the agitator can tear the stuffed animal apart.
But for the washing machines that contain no agitator the stuffed animals can go into the washing machine safely.
You can also just soak the stuffed animals in the bathtub and wash them out and then squeeze the water out of it.
But as long as you put the stuffed animal in the dishwasher on the top rack it's okay to wash the stuffed animal in the dishwasher.
You can wash the stuffed animal in the washing machine as well just as long as the washing machine has no agitator because the agitator destroys the stuffed animals.