If you are going to be on the move through an area that prohibits open flame, then clean water discipline can take some thought. If in this situation, I try to carry a lot of good water from the outset and avoid having to treat if I can. If this is impractical, then you have to accept that your raw water gathering gear is going to be contaminated and must be kept separate from the water you clean.

Starting with a clean filter set, I carefully remove the cap on the output spout and hook up the output tube keeping it from touching anything but a very large clean water container or two. Then I put on latex gloves to set up the intake for the filter pump and begin pumping; I assume touching anything while gloved contaminates it.

When the clean water container is full I carefully remove the gloves to avoid contaminating one bare hand, and with that bare hand remove the output tube and replace the output tube cover. I place hopefully still clean the output tube in its own plastic, water-tight bag. Everything else goes into another waster-tight bag which I assume is now contaminated throughout, along with my hands.

I use alcohol based wipes to clean my hands and hope I only have to process water once this way before getting to an area that allows open flame so boiling water can clean the gear and me.

Edit: extended exposure to the UV in sunlight is supposed to do a decent job of decontaminating see-through components and outside surfaces of your filter set up.