The best Martial Art is whichever one you would enjoy doing the most on a regular basis.
At the end of the day, it’s mostly going to be about exercise and not being a badass or even self-defense. The best thing you can do when faced with danger is to get out of that situation. Most martial arts will not help you a great deal except keep you calm and rational. If someone has a gun, there is no way to remove the chance it will go off, even with a disarm (and that is unsafe for everyone around you). If someone has a knife, there’s almost certainly going to be blood no matter how good you are—although you might not feel it until the adrenaline and blood loss kick in. And that’s without getting into, even if you win the hypothetical fight, knowing what constitutes legal self-defense before, during, and after the fight to ensure you were within those bounds. These aren’t an “always” thing, but most of the time what you get out of MAs is more on the mundane side. Get into a martial arts because it’s something you enjoy, you want the exercise, becoming more comfortable in your body and how it moves, and you want to improve your discipline. And learning how to break fall—that will help you more than anything else because falling can happen anywhere, not just in a fight.
Personally, I do HEMA (Historical martial arts; primarily sword fighting) and traditional archery, because those are what I enjoy and their relevant to a lot of the illustrations and creative endeavors I do. I’ve dabbled in others MAs and there are fun techniques, but I keep coming back to those practiced in the past (mainly European but will reach into as many regions as I can get my hands on) when it comes to my time and money…even if that means having to workshop how they may have worked in their historical context (because for some of them, we just don’t know). Just have realistic expectations with what you choose.
They are not incomparable/incompatible, but each religion will be vastly different in how it engages with socialism. I am what is called a scientific/naturalistic pantheist—which I once had someone sum up as atheism with pagan decor. There is nothing metaphysical in such a worldview, but certainly, there is a different way of looking at the world. You want Heaven? You have to build it. Justice? Again, you have to build it. And rituals are great at communicating with the subconscious—one of the best examples is the “hold your breath for x seconds and then take y gulps of water to get rid of hiccups.” The specifics and values shift based on who you ask, but the folk-idea behind it is widespread and the actions and symbols of the ritual can communicate to ourselves that we want to stop hiccuping. There is the practical safety aspect of taking the time to bow so you can observe the martial art mat, and the ‘spiritual’ aspect of quickly getting your mind in the right state to learn.
I think much of the incompatibility perceived comes from when religion mirrors our present class conditions. “God/s” as kings, rulers, as a grand bourgeoisie essentially. And that’s where the problem can come in because that aspect of more traditional religions is rarely challenged. “God/s” as a grand comrade is a far more interesting concept and one that has more back and forth—there is room to disagree/alter/adapt/learn from/etc with that authority instead of that authority always overwriting the believer’s own instincts (such as on moral issues). I forget where it’s from, but “beware the believer who has never disagreed with their God over anything for their God is an unchallenged mirror.”