Table salt may contain additional unwanted ingredients. Only pure NaCl or minerals found in sea water should go into such a solution. But food industry is allowed to add much more.
Nasal irrigation salt needs just to be NaCl used in isotonic concentration. The indian tradition is based on water from rivers, which is not isotonic and now often contaminated. Clean (sterilised?), potable/drinking tap-water works as well, but appears much harsher than needed. So isotonic solutions are clearly preferable.
One can use kosher regular salt for that. Pure NaCl. And one may be 'lucky' in using all other forms of table salt. But regular table salt is not just NaCl!
Whether sea salts minerals are in there as well is not really that much more beneficial, but when it's regular "table salt" then most jurisdiction allow a lot of other ingredients in it that you do not want in your nose pr on your mucus membrane.
Regular kitchen table salt can be used but is not recommended because of all the additives.
Apart from possible adulterations when using "funny" salts (Himalaya etc) allowed anti-caking agents for example are:
341 tricalcium phosphate 460(ii) powdered cellulose 470b magnesium stearate 500 sodium bicarbonate 535 sodium ferrocyanide 536 potassium ferrocyanide 538 calcium ferrocyanide 542 bone phosphate (i.e. Calcium phosphate) 550 sodium silicate 551 silicon dioxide 552 calcium silicate 553a magnesium trisilicate 553b talcum powder 554 sodium aluminosilicate 555 potassium aluminium silicate 556 calcium aluminosilicate 558 bentonite 559 aluminium silicate 570 stearic acid 900 polydimethylsiloxane
Some of these are listed in the Eu as E170, E504, E535, E536, E551, E559…
Table salt is sodium chloride combined with iodine sources (for nutrition), stabilizers for the iodine, and anti-caking compounds to make it pour by preventing it from absorbing water from the air.
So supermarket bought regular table salt can be quite a bit too irritating for a nasal irrigation.
Further regular nasal irrigation isn't very well supported for most use case anyway:
Karen Head, Kornkiat Snidvongs, Simon Glew, Glenis Scadding, Anne GM Schilder, Carl Philpott, Claire Hopkins: "Saline irrigation for allergic rhinitis", in: Cochrane Database of Systematic Reviews. No. 6., 22. June 2018. doi:10.1002/14651858.CD012597.pub2
But worth a try, imo:
Saline nasal irrigation: Its role as an adjunct treatment
Disclaimer: paranoid germaphobes might want to boil the water before use, to kill any of the germs potentially present in any water, then wait until it reaches body temperature.
Main sources for bacterial contamination are preparing a too large portion of solution and letting it sit and the pots used themselves:
Although common and frequently based on potentially dangerous bacteria, contamination is considered a false problem by some experts. They think that the nasal cavity is naturally full of bacteria and the addition of new pathogens is not clinically relevant.
––Nicola Principi & Susanna Esposito: "Nasal Irrigation: An Imprecisely Defined Medical Procedure", Int J Environ Res Public Health. 2017 May; 14(5): 516. doi: 10.3390/ijerph14050516 PMCID: PMC5451967 PMID: 28492494