I don`t know if off of is used in BrEnglisch or not. I`ll assume not, since su ki says so.
But off of is perfectly standard AmEnglisch. It is not considered colloquial and is not uncommen. He makes a lot of money off of his business. You can leave the of out and it`s just the exactl same thing. With or it it`s the same. Redundant? Not really.
I will guarantee you no native speaking American is going to even hear or notice the difference or care, even if you were to point it out. It is one of the most trivial things to worry about there is for an English learner. If thats all you`ve got to worry about, believe me, you`re going really good. I use the two interchangeably and don`t even notice it. I`d say about 90% of the time she fell off of the horse not off the horse is the most likely to be said, but the latter wouldn`t sound strange to me either. I say don`t sweat the small stuff and think of the two as interchangeable. Understanding is totally unaffected as it is.
It reminds me of what linguists like Noam Chomsky have said, If someone has to teach you something about your own language (native language) the odds are about 100% that what they are teaching you is wrong. Thats why you have to be taught it. Because its NOT your language.
Stackexchange has an English board (and boards for everything from chemistry to gameboards) and people debate ridiculously silly nuances in expressions and words like this. And there are no real answers. Native speakers disagree constantly on things. I see this on the german.stackexchange board all the time. The native speakers can`t even agree on things because languages are fluid and change all the time.
And there are always the language purists who want to protect their language from outside influences. Thats just ridiculous. Example. 40 years ago I was taught you could always say in German das brauchts du nicht zu tun. You don`t need to do that. But it always had to be cast in the negative. You could never say das brauchts du zu tun - the same phrase but in the positive. Now, I`ve heard native German speakers say das brauchts du zu tun. So, the language has changed. Unterestingy enough I read that the exact same rule was appied in English until the 1970s. Prior to 1970, you could never say you need to do that. It had to me you must do that, but you could always say you don`t need to do that. The need to do that came as a result of modern pop psychology suggesting new ways of correcting children in less harsh ways who misbehaved. Instead of scolding a child and saying Don`t do that, pop psychology taught people to say, Johnny, you need to listen to me. I need you to do this. (I read about this in an article saying the Netflix series, Man Men, depicting the US 1960s. The article said the series was accurate in clothes design, cars, etc, but inaccurate in some of the language used back then, as in the example cited). I personally have no recollection if this phrase was used in the 1960s,and I asked my mom about it, who would have been at an age to remember, and she doesn`t recall. Native speakers don`t pay attention to small stuff like this.
They do this constantly on german.stackexchange all the time, with some people saying the phrase das macht keinen Sinn (that makes no sense) is an English import that should abandoned because it likely was adopted in the 1980s, and the better expression is das ergibt keinen Sinn (or das is sinnlos). Trivial nonsense like this is not even worthy of comment. I`ve heard highly educated former German Chancellor Helmut Schmidt say das macht keinen Sinn. Thats why I say only a fool would criticize its modern use. So, the bottom line: ignore the trivia and focus on the important stuff.
Of course, don`t be like the Peruvian translators who posted a sign in Peru in Spanish, (with an illustration of a llama) saying Please don`t feed the llamas but placed the English translation below it as Please don`t feed the Flamingos. LOL.
