If seaweed eliminates methane it likely will affect some gut bacteria more than others. We would not blindly swallow antibiotics affecting what is happening in our gut. There will be side effects one way or another - usually the more effect the more side effect. Seaweed is worth studying and has promise but I'm skeptical when it comes super food claims.
If i read it correctly the paper says the effect comes through bromoform contained in the algae, which inhibits the enzymes participating in the methane production. It's only fed in sub-toxic amounts to the cows I don't think it bio-accumulates, so the meat should be safe for consumption. in other words, it has nothing to do with antibiotics.
I would not be comfortable eating products from a cow fed this without some careful safety studies first.
Otherwise you are potentially poisoning people in exchange for some methane reduction - that's not a good tradeoff.