You can't compare it like this. There are millions and millions of football (soccer) players around the world, but probably only several ten thousands, maybe hundred thousands MMA practitioners. And football is played for hundred years while MMA became professional only 20 years ago and came somewhat to mainstream (still not nearly at a scale like football) maybe 5 years ago.
Non competitive MMA is probably not more dangerous than football, but competitive MMA definitely is. Just look at what's the main goal there - to do damage to your opponent. There is a reason why so many matches in the UFC have to be canceled/delayed.
For "real" fighting, meaning non regulated fighting, I'd rather suggest a good classical (not McDojo) Jiu Jitsu school and some additional boxing. Fighting with cloths on is significantly different to fighting half naked with sweaty/slippery bodies, and in a good Jiu Jitsu school you also learn tactics how to deal with multiple opponents and weapon fighting.
Well of course the overall number of deaths is ridiculous to compare considering the difference of numbers in each sport but considering there has only been one mma death that I know if that has happened in 20 years, the ratio is still heavier on football player related deaths.
In mma you know exactly what the other mans intent is: hurt you. You try to prevent that at all costs. In football you have the intent of controlling a ball and scoring... the injuries that occur in this sport are freak accidents that sometimes come from being blindsided... IMO MUCH more dangerous than mma. MMA events get cancelled and delayed because the fighters get injured in practice... it only take that one guy. In soccer, many people get injured but the match obviously never gets delayed or canceled because its a team sport... much different.
Also, are you talking about jiu jitsu with a gi? No one's clothing is that thick... your clothes would rip if you tried any jiu jitsu moves with a normal t-shirt. No gi is much more practical.