Most people don't need any additional product or ingredient to lower the pH of the soil. Many of the nutrients and amendments that we add to our soil mixes are quite acidic already; so the concern more frequently leans towards getting it back into the 6-7 range. This is why you'll hear so much about dolomite limestone and related materials such as oyster and eggshell which are comprised of primarily of calcium carbonate. These are the most popular organic amendments for adjusting the pH upwards to what is appropriate. Dolomite limestone is calcium magnesium carbonate and so also provides for Ca and Mg (long term) whereas egg/oyster shell is calcium carbonate and provides Ca. When using eggshells, they must be pulverized in order to work faster. The finer the particle size is, the faster the lime can get to work. Ideally you could use both powdered dolomite in conjunction with something less granulated like pulverized egg or oyster shell.
Soil biota do work in our favor to adjust pH, and as the organisms in the soil and the plant utilize what is available the pH will change. Typically you will notice your pH raising for the aforementioned reasons. The exception to this is if your water source generally is of a high pH (above 7) with lots of dissolved solids, as is usually the case in the western states. Check the pH of the water you use, and also check the run-off. If you really do need to help lower the pH of the soil, there are various organic products you can use. Gypsum is a soil amendment that will lower soil pH and provide some elemental sulfur. You can use things like citric acid (lemon/lime juice) and apple cider vinegar as a temporary fix. Add a few drops to your irrigation water and see what difference it makes to the pH. These things shouldn't hinder you micro-life if the usage is kept minimal.
Baking soda in particular I would shy away from using to raise soil pH. It can be done, but consider what baking soda is: sodium bicarbonate. Sodium (Na+) is among those ions associated with something known as salinity. Plants are able to absorb water and nutrients through their roots by having increased salinity within those plant tissues. Another key word here is osmosis, but just realize that if the salinity of the soil becomes greater than that of the plant there will be no uptake of water or nutrient into plant tissues. Bicarbonate (HCO3-) may also introduce some problems because it would rather be with Ca2+ than Na+, if there is enough calcium hanging around. This calcium will become unavailable while the Na+ is free to leach from the solution or go on to form another potentially more detrimental salt. Note that I am not a chemist, but if you are please tell me if I am on the right track with this basic explanation.
There is more to consider in organics when thinking about pH. It is just a measure of the potential Hydrogen of any given solution, but is strongly related to availability of nutrients in the soil. What is considered the appropriate range ( 6.2 - 6.8 ) is where most of our nutrients are available but we can increase the availability of nutrients even if the pH happens to be outside of this range. The best way to do this is by introducing mycorrhizae: a symbiotic fungi that plays various roles for the roots including seeking water and nutrients. Then there are organic chelating agents which include humic, fulvic and amino acids. These are molecules that encapsulate other molecules. They can make nutrients available that otherwise would not have been, and shuttle them into the plant. Unlike synthetic chelating agents such as EDTA, the plant can actually absorb humic and fulvic acids and so they have the added benefit of increasing the ability of the nutrient to move within the plant.