Again, the comparison is moot. Just because you know theory, it takes nothing away from feel. Just like how reading and writing take nothing away from speech. Or how mixing paint takes nothing away from the visual appreciation of a painting. The two really aren't the same thing.
As to rules, actually there are rules. To wit, here's a scenario when I was in college (theory class):
Prof: "You must not use parallel 4ths and 5ths."
Me: [raises hand, prof allows] "Sure you can, I do it all the time."

Prof: "Mr. Lowery, if you wish your music to sound like 18th century classical, you will NOT use parallel 4ths and 5ths."
Me: [sinking below desk top] "Uh...ok, I see what you mean."
Point is, different styles have different things about them that make them sound the way they do. AND, in fact, unless you DO KNOW theory, you will not be able to reproduce some of those styles if they are something from times past when there were absolute strict rules for writing (such as in many classical works). PLUS, when you DO KNOW theory you will also be able to understand other styles that were not written by hard rules (like Delta blues).
So, how do you play Delta blues anyway? If you know NO theory, you can listen and try to get it close to what you think is going on. If you DO KNOW theory you will take the listening further by recognizing just exactly WHAT is going on, and then you will KNOW. It will even help with the feeling to have a greater understanding like that.
I get mad when I hear someone put down knowing theory (I don't mean that that is what's going on here in this thread, it's not). I also get mad when I hear someone boast about how they don't know theory, as if that's something to be proud of. And then, I get flaming mad if I ever hear anyone boast about how they do know theory, as if that is also something to be proud of.
Theory is just knowledge. If you don't know it, that's fine. But, I don't know why any musician wouldn't want to know it.