You are like me, I had congee once in China that was virtually inedible for me because there was pieces of ginger spread throughout and I absolutely hate hate hate ginger, and I am Chinese. So, I believe I can provide you with some very practical answers.
By mung bean soup I think you mean congee/zhou/粥?
First, what is your actual problem? Do you hate the taste of ginger altogether, or just don't like biting it? If you don't like biting it, then you can use ginger powder. I can detect tiny pieces of ginger even if you chop it finely or grate it so that is not an option for me. You will have to experiment with the quantity because fresh ginger tastes different to several-days old dried ginger (by dried ginger I mean after you cut a piece and leave the rest in the fridge or outside, not actual 'dried' ginger as in, dried fruit) and probably to ginger powder. I use whole pieces of ginger slices so I can pick them out except in meat fillings for dumplings and baozi.
Second, what I use ginger for:
I use ginger in all meat products (meat = non-vegetarian and therefore fish) to get rid of what we call ‘xing', or a fishy/bloody/meaty flavour. A little bit of ginger (fresh or powder) plus cooking wine gets rid of the xing flavour, too much and you will actually taste the ginger. Trust me, I can taste and smell it. I do not use it in anything else. For meat fillings, you can use ginger powder so you will not have a chunk of ginger in your dumpling or baozi.
Third, a solution. If you want the fishy flavour eliminating power, then simply use whole larger slices instead of dicing them or grating them. Grating them will spread out the ginger in your entire dish and every mouthful will have it. You can easily pick out the larger slices. This is good if you need to stirfry the ginger first. If you need to boil the ginger as in your case, put your ginger in a cotton gauze spice bag and tie it up - the flavours will diffuse into the soup but your ginger and other spices will stay in the bag and you can pick it out in one go afterwards. Just use the right amount of ginger according to taste (you will need to experiment), a little to eliminate xing flavour, a lot to actually taste the ginger itself.