How many glass filters do you usually carry with you? I normally take a couple of polarisers in different sizes along with three or four step-up rings so that I can cover all my lens' filter threads. I don't use the original plastic boxes as they're too big, but I've got a number of the older, round boxes, that filters used to come in. (You can usually pick these up cheaply at second hand equipment fairs.) I then slip the filters and step-up rings into the flat rear pocket on my bags or in the laptop/tablet pocket, which in my case is otherwise unused.
If I need any other filters, such as grads etc. I use square resin filters in a filter holder, but these do take up space in the bag. Most of the time I prefer to apply graduated filters in post.
You could also put the filters individually into clear, zip-lock plastic bags; not much protection, but no additional bulk or weight. However, if you used the laptop/tablet pocket in your bag, as I do, they would be well protected.
Like @Hannety I love metal stack caps and typically I am not carrying around a boat load of filters or lenses. So if, for example, I am going out with my 12-100 PRO or old 4/3rds 12-60 SWD which both use 72mm filters, I can easily screw together a polarizer and a 3-stop ND filter with metal caps on both sides which can be carried in a pocket or bag and is a super resistance to damage (even when you have it in your back pocket and sit on it, your butt is what hurts).