Mat 15:11 Not that which goeth into the mouth defileth a man; but that which cometh out of the mouth, this defileth a man.
Mar 7:15 There is nothing from without a man, that entering into him can defile him: but the things which come out of him, those are they that defile the man.
1Co 8:7 Howbeit there is not in every man that knowledge: for some with conscience of the idol unto this hour eat it as a thing offered unto an idol; and their conscience being weak is defiled.
1Co 8:8 But meat commendeth us not to God: for neither, if we eat, are we the better; neither, if we eat not, are we the worse. 1Co 8:9 But take heed lest by any means this liberty of yours become a stumblingblock to them that are weak.1Co 8:10 For if any man see thee which hast knowledge sit at meat in the idol's temple, shall not the conscience of him which is weak be emboldened to eat those things which are offered to idols; 1Co 8:11 And through thy knowledge shall the weak brother perish, for whom Christ died? 1Co 8:12 But when ye sin so against the brethren, and wound their weak conscience, ye sin against Christ. 1Co 8:13 Wherefore, if meat make my brother to offend, I will eat no flesh while the world standeth, lest I make my brother to offend.
What these verses tell us is what the verse you mentioned condenses into one verse. Nothing you put into your mouth can defile you. But, there are those who are weak in knowledge who think that there are things that can defile you. If you are with that person with little knowledge who thinks something is wrong (ie drinking alcohol in the presence of someone who attends a Baptist church), then you weaken your message by partaking of the item which they think defiles you. So, do not partake of that item in their presence, so your message is not hurt.