Plastic 'taste' comes from plastic molecular fragments. That means that your water system probably has components that arent compatible for POTABLE (drinking) water.
These fragments are unbound or uncured monomers that arent 'attached' to a long chainn polymer ... most are quite unhealthful, many are carcinogens or agents that attack the central nervous system. Fiberglass tanks will emit styrene monomer for the lifetime of the tank; cheap plastic/rubber hose will continue to emit and oxidize for the life of the hose; the cheap (typically green) PVC dock hose will emit PVC fragments until you throw it away .... all examples of materials that shouldnt come in contact with potable or 'drinking' (or washing) water.
First, get rid of the that green 'garden hose' and get (a white one) thats rated for potable water.
Condemn any fiberglass water tank used for drinking .... such can be 'lined' with low amine epoxies rated for 'potable water'.
Any system water hose that has turned 'yellow' --- out/replace with new & rated for potable water. If it doesnt say 'potable water' service, its not for potable water service.
Once the 'hardware' of the system is validated, then get inside the tank and mechanically scrub it. It is of absolutely NO use to 'sanitize' a fouled water tank, a tank has a LARGE bacterial colony growing on the internal surfaces as all the chlorine/clorox will do is kill/stun the surface layer and totally leave the 'deeper' microorganism alive and which will cell divided to continue the massive colony/infection.
The proported RV specs. for sanitization of RV systems are for the sanitizations of NEW or CLEAN systems .... certainly NOT for a system that has a developed 'bio-film' (the slipperiness that one feels when one wipes fingers across the walls,etc. of a water tank).
Other 'stinks' that can mimic 'plastic taste': certain molds and mildews of the Aspergillus Family ... some species of this family are quite toxic. They must be scrubbed out then the tankage sanitized .... no other way to do this.
Lastly, clean or replace the ENTIRE tank vent line ... will probably be the 'seed/spore 'container' for constantly re-inocculating the water tankage. You will probably projectile-vomit when you see what's growing in that vent line. Then put a bioblocking 0,2µM hydrophobic filter somewhere near the 'intake from atmosphere' to keep the tank from aspirating bacteria, mold and mildew into the tank everytime you open a spiggot.
Sanitization (10-15 ppm chlorine for at least 1-2 hours) is only done on a *clean* or new tankage and its distribution. Sanitization wont 'clean' a tank ... and those inactivated or killed cells remaining will rapidly become the nutrient source for successive infections of bacteria, etc.
Treat you water tankage like you do with your dishes, pots and pans, water containers, etc. ... like you do at home ----- keep it "hygienically clean". You certainly dont dip your dishes in diluted clorox then put them in the cupboard do you?
The advice given for keeping a minimum amount water in your tank sufficient for immediate needs ... is good advice.
Forget carbon filters .... all carbon filters do is concentrate the fragments and when the adsorption to the carbon is complete (and there is no way you can tell without 'instruments') you still get the 'plastic taste' plus bacteria readily use the carbon as a nutrient source ... and then you have to think about all the harmful chemical fragments that simply passed through the carbon filter ... and the 'dilution' is so great that you can no longer 'smell' them ... but are still there.
If you have stinky water that your nose can detect ... you have a major problem that no deodorant, or witches brew will ever solve; but, using such 'masks' will only 'mask' the presence of a potentially BIG problem. Simple answer mechanically clean/scrub the tank, replace all non-potable rated components, etc. ... then sanitize a clean system.