What word should I use in informal speech for connecting cause and effect just like から does in polite form?
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Use から. It's not only used in "polite" speech (it doesn't actually matter what you mean by that), but also in "informal" speech.
If から reminds you too much of K/J-Pop, you can sometimes replace this から by ので/んで e.g.
but you'll likely end up sounding more polite than when using から.