at first glance only options D and E would work, "many of" is the correct way, not "much of" and E is correct.
many of the currently uncontrolled dioxins to which North Americans are exposed come
"to which North Americans are exposed" is the correct way to say what you mean, if there were "to" after "exposed the sentence would be wrong.

'That' is a conjunction for;
for example, He told me that the book is a good read. we can see that the conjunction 'that' here connects or unifies the two clause.
option A is incorrect because of the connecting figure 'to which' it does not properly connects the two clause of the sentences. Also, the usage of 'much of the currently uncontrolled dioxins' which is use to express great deal of something, is suppose to attract a plural verb and not a singular (comes) as being used in this option A. The use of plural verb 'come' further makes this option valid.

in Option B. from the explanation above 'that' is used for introducing a clause which is the subject or object of a verb (such as one involving reported speech), or which is a complement to a previous statement. Thus, this option justifies the proper usage of 'that'

in option C, The option is guilty of tautology and does not follow normal regular parallelism. 'that are' and 'and that'. thus the option is incorrect.

Remember 'many is use for countable nouns'
option D, the option is incorrect because of the use of 'many' (for a countable determiner) and remember that dioxins are uncountable which makes 'many' inappropriate to use.

in option E, this option suffers the same fate as option D. As the use of 'many' renders it invalid.