First of all, I don't think this is a matter of "so" at all. It is essentially the issue of commas with coordinating conjunctions: FANBOYS.
Yes, when two independent clauses are connected with a conjunction, a comma is often used. This is not a strict rule, but a general guideline (note how I used a comma before 'but' even though it is not needed/recommended there—I used it there just to reflect a pause in my speech; in a formal context, I would not put the comma there).
It is a good idea to follow the guidelines when you are writing something formal (e.g., academic papers, college applications, official reports, emails, etc.) and then be consistent throughout your work. When you are writing something that is informal (fiction, emails, ELL answers, etc.), feel free to use punctuation to convey your tone (e.g., comma to denote a pause in speech).
In this case, the use of comma has nothing to do with AmE or BrE. The only time a "comma" has something to do with AmE/BrE, is when it's an "oxford/serial" comma.
Oh well, let me now state the "rule":
If the two independent clauses (compound sentence) are short and closely related, you may omit the comma. Source: Commas and Independent Clauses
However, do not omit the comma if doing so creates ambiguity. The most important thing is clarity.
Here is something from an authoritative source, The Chicago Manual of Style Guide, 17th ed. (emphasis added):
When independent clauses are joined by and, but, or, so, yet, or any other coordinating conjunction, a comma usually precedes the conjunction.
If the clauses are very short and closely connected, the comma may be omitted (as in the last two examples) unless the clauses are part of a series. These recommendations apply equally to imperative sentences, in which the subject (you) is omitted but understood (as in the fifth and last examples).
- We activated the alarm, but the intruder was already inside.
- All watches display the time, and some of them do so accurately.
- Do we want to foster creativity, or are we interested only in our intellectual property?
- The bus never came, so we took a taxi.
- Wait for me at the bottom of the hill on Buffalo Street, or walk up to Eddy Street and meet me next to the Yield sign.
- Donald cooked, Sally poured the wine, and Maddie and Cammie offered hors d’oeuvres.
but [no comma in these]
7. Electra played the guitar and Tambora sang.
8. Raise your right hand and repeat after me.
Source: CMoS, 6.22: Commas with independent clauses joined by coordinating conjunctions