I want to do Brazilian jiu jitsu and tae kwon do at the same time. However, I’m worried that they might not work together and be problematic.
This is actually two questions you're trying to answer. The first question is: Will it be too confusing to learn two styles at the same time? The second question is: Are the two styles compatible?
My general answer to the first question is that it's only confusing if the two styles are very much alike. For example, taking Judo and Brazilian Jiujitsu together might be confusing, because they both have similar techniques. There's a significant amount of overlap between the two styles, and yet the strategy and focus of Judo is very different from that of BJJ. That can lead to confusion.
But taking Taekwondo and Brazilian Jiujitsu together shouldn't cause any real confusion, because they're completely different styles with very different techniques. There's almost no overlap between them.
As for the second question (compatibility), what you're asking is whether or not combining Taekwondo and BJJ will be compatible in a way that Boxing, Muay Thai, and Kickboxing are compatible with BJJ, as seen in modern MMA. The answer is a firm MAYBE. Let me explain.
Whenever you talk about compatibility in martial arts, you have a goal in mind. That goal may be making an effective street fighting martial art, or it might be making something that works in competitive MMA fighting. You may even have another goal in mind. Who knows. Now, that goal determines everything about how your combined martial art will look. That's because the "rules" of the game shape your training, and your training determines how your style looks.
Take western Boxing for example. By itself, its stances are upright. Feet are a shoulder's width apart, generally. There are no wide stances. In Brazilian Jiujitsu and MMA, you're going to see a wider stance, with a slight lean forward of the body, and with a bit of crouching down in the knees and hips. There's a reason for why the Boxing stance looks very different from the BJJ and MMA stance. It's because in Boxing, you don't have to worry about your opponent rushing in and trying to grab your torso or your legs for a take-down. The rules of the game determine the way your martial art looks.
So to generalize: The more similar two styles are, the more compatible they are but the more confusing they are to study at the same time. The less similar they are, the less compatible they are but the easier they are to study at the same time.
Taekwondo forbids strikes below the belt and anywhere to the back. It usually forbids punching to the head (kicks are allowed to the head, however). There is no grappling allowed, either. As a result, Taekwondo's stances, techniques, and strategies will look very different from what you'll see in something like Muay Thai, where kicks below the belt are encouraged, and punching to the face is allowed. In particular, training in Taekwondo can create bad habits that leaves your legs and head open to attack, since you're not training to defend against those techniques.
So at first glance, you might be tempted to say that Taekwondo and Brazilian Jiujitsu are completely incompatible. Because, they are. They are designed for completely different situations, and so they look completely different. But guess what? The same is basically true of Boxing and Brazilian Jiujtisu. Yet, Boxing and Brazilian Jiujitsu together have been successfully incorporated into MMA training. How?
Well the answer is that someone had to think about how to adapt both Boxing and Brazilian Jiujitsu together in an intelligent way that addresses the rules of competitive MMA. Both styles had to be modified in order to make an MMA style that worked, given the rules of competitive MMA fighting.
Nowadays in competitive MMA, we are seeing Taekwondo coming into play here and there. It's because a lot of MMA people probably grew up learning Taekwondo when they were kids. They're taking small amounts of Taekwondo that they learned and are applying it in MMA when it makes sense to do that.
And they didn't just start out trying to combine TKD with BJJ. They usually take BJJ, Muay Thai, and a separate MMA class. That forms their foundation. From there, they add whatever else they want to add when they feel comfortable enough that they can do that. Most of the work of adapting everything to fit MMA has already been done for them by countless numbers of people who came before them. When they want to add some tiny thing to it, they can do that fairly easily at this point, usually in MMA sparring sessions where they get to make mistakes and learn from them.
So, I'll give you some advice. Don't try to combine two different styles to make your own MMA style in a vacuum. While that may be intellectually very interesting, challenging, and satisfying, you're just one person. The MMA training that exists out there already is so far ahead of what you'll come up with on your own, in all likelihood. If your goal is to be good at MMA fighting or street fighting, chances are you'd get there faster by just going to a good MMA school and learning what they have to teach. Then you can branch out after forming a good foundation.
Otherwise, you're going to have to do a lot of work to learn what MMA has already learned. You're going to make all of the mistakes that people made in MMA from the beginning. If you look at the evolution of MMA fighting from the early 1990's with the first UFC until now, you're going to realize that those early MMA fighters really wouldn't stand up against the MMA fighters of today. That's because MMA has evolved and gotten a lot better. So learn from them. Why not?
Let me just wrap it up by saying that Taekwondo gets a bad rap from pretty much everyone else in martial arts. That's primarily because of the way it is trained. Sparring in TKD is done with light contact, aggressive offense is emphasized (defense is almost an afterthought, to the point of even letting their arms fall to their waist), and the rules don't permit the vast majority of typical self-defense scenarios that you might encounter in real life.
However, if the training is modified such that all those issues are addressed, then Taekwondo is no longer a problem. The problem is shifted from the style to the training instead. Is it really TKD at that point, though? Sort of. It starts off with the same techniques, but like with Boxing and BJJ, everything will need to be modified to handle the different rules. What you end up with might look a little like Taekwondo still, but it will be vastly different overall.
Hope that helps.
Those two were my first martial arts, but not trained together. They are compatible at the same time because they are so different, you can be resting by training. Your legs tired, go do jujitsu. Body feels broken do tkd that night. Now if you've never practiced a martial art before, stick to just one for the first two years. Beyond the styles, you need to learn your body and how to train yourself.
For everyone else who was talking smack about tkd having no real purpose on the street because of the Olympic style rules, there's military tkd and it's all groin, eye and throat strikes. Works way better against multiple attackers than jujitsu. And even more so for MMA look at all the champs, they are wrestlers not jujitsu guys. So if you want the best martial art for MMA go with American wrestling.