Righto, i only use a leather strop, i have made fabric strops, and have been given one with a fabric component that i do not use.
My first strop is a homemade one that i used to palm rub for a while, but now only do rarely, it is 3" wide, on that i dont really do an X more of a windscreen wiper type stroke, which feels quite natural, start toe leading (slightly), finish heel leading (slightly). I get a pretty good edge from it.
My second strop (a recent gift) is 2.5" wide, that was hard and felt abrasive when i got it, i used 2 applications of leather conditioner (bought for my boots) and rubbed each in well. On that strop i do an X, but only because i have to, and get good results.

I dont think an X is necessary if you dont need to do it, and can do something other than just rubbing the blade up and down. If the leather feels hard then either palm rub or add a little conditioner, but remember that what you put o cant be un-put on.