It would be difficult to come up with an interpretation to the assertion that people who wear cloth made of two fibers should be stoned that didn't make the statement look ridiculous, but, then, if you know of one, by all means, let's hear it.
I believe there is a very important lesson for you here. Maybe several. Did you hear that from someone? Maybe on an anti-theist website? Don't believe everything you hear. Check things out for yourself. If the people who have studied the bible all their lives are telling you that it's main message is one thing and the people who wrote an anti-theist website have demonstrated time and time again that they put in a lot of effort but little thought it might make more sense to listen to the one group and not the other. And of course to evaluate everything first hand.
Somehow you have internalized a set of beliefs about the bible that lead you to reject it wholesale and to think that it is full of ridiculous stuff. And as a result you have posted the statement above. You might want to reconsider all of what you think.
So, the explanation for that passage is very simple. I found it in Leviticus 19:19 and in it there is absolutely no instruction to stone people who mix cloths. Is that good enough?
Regarding the rule itself: consider the context. Just about every rule in that chapter points to two things that must be kept separate (which is another word for holy).
For example:
Do not make idols; I am the Lord. The contrast is between false gods and a real God. They are separate.
When you make an offering do it in an acceptable way not an unacceptable way. The contrast between holy and unholy is obvious.
When you harvest a field take the center but leave the edges for the poor. the contrast is between a part for self and a part for others.
You can read the whole chapter and see for yourself that just about every verse in it makes a very clear contrast pointing to a separation. Some are not so obvious; I wonder if the pattern faded in translation.
Another thing that seems to be a pattern to me is that some of the verses are short and direct but then the next verses follow up with more detail.
For example, verse 11 is:
'Do not steal.
" 'Do not lie.
" 'Do not deceive one another.
And then it is followed by several verses that expand the concepts with more detail. "'Do not pervert justice; do not show partiality to the poor or favoritism to the great, but judge your neighbor fairly. " Again the contrast between holy and unholy is still there.
So why is there a short and direct verse about 1) mating animals, 2) mixing seeds, and 3) mixing cloths? Do you suppose the verses that follow will add more detail?
(I have added numbers)
1) Don't sleep with a girl promised to another [the obvious unspoken contrast is to only sleep with girls promised to oneself]
2) When you enter a land do not eat the fruit there until three years later [to allow the trees to mature and reproduce] so the harvest will be increased.
3) Do no eat meat with blood still in it. [shows the contrast between death and life]
I propose that the visible signs that could be seen in ones flock, ones field and ones clothing would reinforce the other laws of separation. Every time one put on an article of clothing one would be reminded that the Israelites were not the same as the people living around them; they were a holy or separate people. They were charged with and chosen to keep the written law that pointed to Christ so that in future years everyone would be able to see how Christ was pointed to in advance. But if as a nation they became just like the nations around them they would never be able to fulfill their charge. All the holiness laws can be seen as separating the Israelites from others. A good Hebrew woman would never marry a man who was not circumcised. A good Hebrew family would never eat with those who did not prepare their food Kosher. And it would be really easy to know who was who based on how they dressed and conducted their lives.