You would not use the phrase "no matter what" in that case. It does not mean "whether" - it means "always".
You could say
I will love you no matter what.
Which means "I will always love you, even if the situation changes".
The original sentence is wrong, or at least sounds strange.
If you want to say "many things are different in different cultures", you could say
Travel lets us experience different cultures. Whether dietary habits or architecture, they are different from country to country.
But here, "They" would mean "different cultures". I think you're using it to mean "dietary habits or architecture", which is wrong in English.
Finally, you'd actually use "lets", not "let's". "Let's" would be short for "let is", which doesn't make sense.