In response to the question, "Is it OK at a competitive REL event to riffle shuffle an opponent's deck?", tell them the truth.
It's legal and is one of, if not the most efficient way to sufficiently randomize a deck.
Because man do people get really upset by the notion that you might shuffle their deck.
But you can and I personally believe that at competitive events, you should.
I also believe that people should shuffle those decks with care, being considerate of other people's property.
Finally, I think that if you're at a competitive event and you don't have your deck in really good sleeves to prevent wear and tear and to help them stand up to shuffling, then you are the one who is being a fool, not your opponent.
I realize that this notion isn't popular. However, WotC has already agreed that riffle shuffling is legal and the math has been done on the riffle shuffle proving it's the one of -most likely the- best ways to randomize a deck. If you have an issue with that, take it up with WotC and the laws of mathematics. It isn't my problem.
Now all that said: three things.
First, a perfect mash shuffle can replicate a riffle shuffle. However, you have to perform it more times in order to get the deck randomized because odds are you aren't doing a perfect mash shuffle, and in a timed match that's important. It also means more wear and tear on those cards, just from a different angle. Again: good sleeves, people.
Second, it was pointed out to me that most of the studies and research I found used the riffle shuffle because it is the most common way to shuffle cards, at least in America. I will admit that there might be a space for research into mash shuffling to see exactly how many mashes it would take to get the same kind of randomization that seven riffle shuffles do. From what I understand, it's definitely more but how many more, I couldn't find.
Finally, it is worth pointing out that randomization is the goal here but it must be done with consideration of the investment that players put into their decks. Do I want my opponent's deck randomized? Absolutely. You should too. Do I want to put a crease in their Gaea's Cradle to do it? Hell no. I don't even want to put a crease in their Island.
So: respect people's property and their desire for an honest game. Sleeve up your cards, shuffle them properly but gently.
Seems pretty reasonable.