I've not heard that one cannot wash water resistant items in a HE machine. I can think of no reason that this would be the case.
Also, some of the items you list are not what I'd consider water resistant. In my experience, water resistant refers to outer wear designed for wear in the rain. And those, unless specifically treated, may lose their resistance when washed in any machine or even by hand.
The spin cycle is faster in a HE machine but I've not found that it negatively affects any of the clothes. I do wash bath mats, allergen pillow covers and mattress pads in my HE machine. There are two types of allegen pillow cases and mattress pads. It may be, if they're plastic, that spinning them would cause creases to set but I don't know that it would affect their performance. If it does then I suggest you wouldn't want to spin them in any machine and I've not seen that mentioned on their product label.
Here is a site that says not to wash water resistant fabric using a detergent and to always follow the fabrics washing instructions. No mention of the HE washing machine. http://www.wikihow.com/Wash-Water-Resistant-Fabrics
I googled "HE machines and water resistant fabric" and did not find a site that says not to use a HE machine to wash them. One site did say that high speed spinning can stretch the fabric but I don't see that that would be a problem with the items you're listing.