Many causes for 'plastic taste'
If your tank is plastic, its probably polyethylene which is quite inert. But there maybe many 'plastics' in boat water systems that arent so inert. Especially the hoses or other components may be 'breaking down' from age or by the action of micoorganisms (using those plastics as 'food') and should bear some investigation. Also some microorganism all by themselves will issue 'taste' into the water that is similar to a 'plastic taste'. The typical 'carbon' thats found in 'water filters' isnt all that applicable nor efficient for removing 'organic' molecules, rather they are primarily for removal of chlorine and other 'inorganics'. For 'organics' removal, to 'decolorize', etc. you need quite different carbons than found in a 'Home Depot' to do a good job. 1. First, examine your tank to see if its fouled with a visible 'scum' or *slime* (bacteria colony - calcyx or large colonies of 'fungals'). .... just reach into the tank and feel for any 'slimey' feel of the tank walls. Such large colonies usually require that you mechanically scrub them free from the walls and surfaces. Shock sanitizations with chlorine, etc. compounds will usually only kill the upper layers of these slimes and leave the deeper sections still viable and alive. For extensive fouling in tanks that cant be opened *many* repeated shock sanitizations are needed .... problem is if you cant open and inspect the tank there is no way to tell that the bacterial, etc. slimes are actually removed, even after many successive shock sanitizations. Leaving DEAD cells in the tank only allows these dead/stunned microorganism to eventually break apart and slowly dissolve into the water upon 'decomposition'. Leaving a lot of cells on the walls only provides nutrient sources for successive infections of other species. What was described by some other posters is how to sanitize for a NEW system or a system that is relatively clean. For frank (visible) bio-fouling you really need to mechanically scrub the microorganisms off the walls, piping and then when 'clean' perform a shock sanitization --- and that requires large enough access ports on a tank so you can reach in with a scrubbing brush, strong soap and water, etc. If the tank has NO access ports and is visibly fouled you really need to do many many repeated shock sanitizations. 2. Most plastics are not fully polymerized and will contain unbound 'monomers' that constantly leach into the water; plus, if they are not 'stable' in water (many are NOT) will eventually begin to breakdown into molecular fragments ..... taste! Hosing, tubing that is discolored or internally 'softened' are prime sources for chemical 'emissions'. Some fungals will break down the smooth surface 'skin' of many plastics and enhance the decomposition process of the 'plastic'. Hint: remove and replace any hosing that becomes 'discolored'' or feels 'soft' on their internal surfaces that come in contact with water; and replace with components that are listed 'safe' for use with POTABLE WATER .... if no listing evident in the 'specs' then dont use it. There should be a NSF or FDA rating to be compatible with POTABLE WATER on most 'plastics'. 3. in most cases of boat tanks that have been in service for any time the **vent line** will become a massive incubation site for microorganisms ... and their 'spores' will get sucked down into the tank every time the water is drawn drawn from the tank. If the vent line has any evidence of discoloration, has a large visible colony of microorganisms growing ... especially the really BAD 'black stuff', simply replace the vent with new. To prevent or lessen contamination in the vent simply put a large wad of 'bandage cotton' over the end, cover with a few wraps of bandage gauze and 'keep dry' .... Replace yearly. You can obtain commercial small bio-blocking hydrophobic 'vent filters' from 'scientific catalogue' sources. Yes, definitely clean and or sanitize the tank but do consider to remove / replace any plastic component that shows any visible degradation or discoloration. The goal should be a CLEAN system, not only a system that has had 'sanitization'. 4. If after thorough mechanical cleaning and multiple shock sanitizations you STILL have that 'plastic taste', then suggest that you do apply a carbon filter (any carbon filter) ... install a small pump and continually pump the tankwater through the carbon filter and back to the tank (slower flow through the carbon is 'better') anytime that you are on the boat (and if you have the excess battery/power capacity). This will help 'strip' the objectionable 'organics' from the water. (The probable best carbon for 'organic stripping' is "Darco G60".) If your water is chlorinated (and it should be to keep the 'growth' down to acceptable limits) you will have to change the carbon filters often even if the flow to the carbon filter is nil or zero ... as the carbon will (by chemical equilibrium) continually remove the chlorine. Carbon also accelerates bacterial growth (many micro species use the carbon as 'food'), so 'carbon filters' should be changed 'often' as usually there will be a large bio-colony living on it. Try HYGIENE, then if needed - carbon stripping. BTW if your tank is 'fiberglass' and it isnt 'lined' with a specific NSF/FDA rated 'potable' epoxy, then either rip out and reinstall a new tank ... or 'line' the tank internals with the proper 'potable water grade' of epoxy, etc. The 'styrene monomer' that continually emits from 'fiberglass' is VERY unhealthy. When your tongue and nose tells you 'plastic taste', strongly heed that warning as such 'leachables' can be very harmful upon long term exposure. Hope this helps.