プラスチックには体に悪い物質が付きやすいため、魚などがプラスチックを食べると、その魚を食べる動物や人にも悪い影響が出る心配があります。
As for plastic, because bad materials easily stick in the body, there is a worry that if fish eat plastic it will also have a bad effect on the people and animals who eat those fish.
I can't understand the purpose of the に in bold at the start of this sentence.
Can it be omitted without changing the meaning?
You seem to have failed to parse this sentence correctly. Treat 体に悪い物質 as one set here.
プラスチックには[体に悪い物質]が付きやすい…
[Substances which are bad for your body] easily stick to plastic, ...
AがBに付く is a common way to say "A sticks to B," and it's not the body but plastic that bad substances stick to. So に after プラスチック is just "to" as in "stick to ～", and に after 体 is "for" as in "bad for ～".
The topicalizer は always replaces が/を, but it doesn't usually replace に/へ. See this.
You can omit に in this case without changing the meaning. But I wouldn't do so because this section is relatively complicated and omitting に may make it a bit harder to understand. See: When do you use は/に for どようびは/に?
