isn't Karate the linear one and TKD the circular one?? hah
I don't see a major problem with cross training the arts. The stance in Southern Praying Mantis (SPM) isn't something that is completely opposite to a stance taken in TKD. Though they do preach and train to have their feet firmly grounded and rooted to the ground unlike TKD (at least sport TKD) where you see guys bouncing around without too firm a grip on the ground (results in slippage and loss of power).
The stance is pretty natural and most likely won't interfere with your TKD training. But the best thing to do really is go take a class or two to get feel of how the movements are and if they suit you. Personally, the training in SPM has never really had any conflict with anything else that I've done, whether its kicking, punching or grappling. So I don't see why you can't cross train between TKD and SPM. Goodluck!
"you're going to work till you wish you were dead and then keep going.."