Like you, I find the latter really quite unpleasant (to the point that I really am surprised anyone willing eats San Franciscan sourdough). But wild starters can range from tasting just like ordinary commercial yeasts, to tasting similar but with a richer flavour, all the way to the funk that we both dislike.
I have never had a San Franciscan sourdough in Europe, so I doubt that this sourdough is the nasty (to my taste — many folks love it) kind, but maybe there is some subculture of inedible (again, to my taste) European breads. More likely, I suspect that this is just a good wild starter.
Use baker's yeast instead. That doesn't limit you to basic recipes -- there's a vast range of interesting stuff you can bake. You'll usually need to make a preferment with flour, water and yeast (a "poolish" or "biga") so the overall routine is very similar to sourdough.
My wet sourdough is 1 part flour to 3 parts water. As noted in a sibling comment, this favors the sour parts (lactic acid?), but compared to a dry starter, there are significant advantages the the starter/yeast combo:
1) Feeding the wet starter takes 10s: pour flour and water onto leftovers and stir quickly with a spoon. No sticky stuff to deal with.
2) The starter seems exceptionally stable, maybe because of the water layer: I only wash my starter jar every two or three months, and the 10g or so that I put back in the fridge after starting a dough, will last for weeks and consistently restart overnight when fed
3) Being able to independently adjust yeast-levels in a predictable way, means that I can easily play with sourness levels and adjust leaving times when I have to match the timings with other activities.
There is the downside, of course, that I need to keep bakers yeast in the house as well...
I also prefer less sour breads and since I started using a stiff starter it's much better than more liquid ones. I still haven't found the perfect recipe yet but it is possible.
A good intro into the difference of starters is at the bread code: https://www.the-sourdough-framework.com/Sourdoughstartertype...
I think the main factor for this is how "mature" your starter is.
After feeding your starter it will expand, then collapse, then grow more sour. I generally time it so that my bread isn't as sour.
If I am baking soon -- larger leftover starter and smaller feed. if I am baking tomorrow -- tablespoon or so of starter with bigger feed to get my leaven.
Or bake a basic no-knead loaf. I would mix the dough in the morning and bake it in the evening.