Yes, it can be washed.
There are broadly two methods of cleaning. One is cleaning through friction with a brush, and the other is dissolving and removing dirt with a solution such as detergent.
The washing machine will be the latter, but stains that are strongly adhered require cleaning through friction with strong pressure, and it is necessary to use them separately.
In other words, because they are washable in a washing machine, it means that the insides of the shoes can all be washed.
It's the same as not having the issue of being unable to wash the back side of a T-shirt even with a regular laundry. When it comes to clothing, washing with a detergent solution is sufficient and doesn't pose any problem. However, since shoes tend to accumulate dirt that requires brushing, there are specialty laundry nets like "ZUKKURIN NET" that are designed to allow for friction washing in a washing machine.