There is a long answer to this question. And a short answer. Let's start with the short one.
Because pronouncing clothes the same way as close is easier. So that's what many Americans speakers of English do. They go shopping for new clothes /klos/.
The longer answer is that the th in clothes is voiced: /ð/. And, according to the standard rule for s endings, that means so is the ending in clothes: /z/.
Now, I ask you. Who has the time or energy to pronounce a tricky consonant cluster like /ðz/? Sure, you may hear some over-achievers tackle it, but for most of us, we are perfectly happy to lose the /ð/. Why trip over a dreadfully difficult consonant cluster if you don't have to?
Many times, students have asked me why a word in English is pronounced one way or another, and sometimes it just comes down to the short answer: it's easier.