Fluoride is a natural ingredient. sodium fluoride is found in the healthiest natural spring waters and is a product that binds with the enamel of teeth making them stronger.
Fluoride has been added to toothpaste since the 1950s, the reason for adding it is because most city water "purification" plants removes the fluoride naturally found in drinking water. Fluoride has been removed from drinking water since the 1930s when some quack realized that fluoride is an effective rat poison, so the processing plants were designed to remove it, only to later discover it is a natural ingredient needed for healthy teeth and now we have to pay extra to get it. Unless you are fortunate to live on a farm and use well water, which has not had the fluoride removed.
Organic is fine, however there is no such thing as non-organic foods. Organic simply means "from living organism" or in the case of organic chemistry it refers to the branch of chemistry relating to molecules that form carbon chains.
The term "Organic" has become a catch phrase of the advertising media and is used to sell low cost items at a high price. All vegetables, fruits and meats are "Organic" products. I think people confuse the word organic with natural. But the only way to get natural food is to either harvest it in the wild or grow your own. Even then to be fully natural you would have to avoid wheat and corn. Corn has been cultivated for so long "wild" corn no longer exists and nobody even knows what plant it originally was but most people suspect it was originally teosinte. Same with wheat, except wild wheat still exists but it is essentially inedible.
As far as using the miswak or siwak. It is good to use. However keep in mind that it it is a generic term and is not a specific plant. Miswaks are made from very many trees some of the more common being: Arak, peelu, orange, walnut and olive
It is also called "Kay Sugi" (Chewing stick) In Saudi the tree most used for a miswak is the arak or peelu. Also used in Saudi are olive and walnut tree. The Arak is a variety of Magnolia. It has been found that the sap of the magnolia is an effective anti bacteria. The Native Americans used Magnolia, Pine, Juniper and Birch trees as miswaks.
I believe the British and Europeans used birch most often. The miswak has been used by all people of all faiths and in all lands until the invention of the artificial toothbrush in the 1920s or so.