According to Machado et al in 2016, the overall nutrition of the rumen, quantified in vitro, has no apparent negative effects while methanogenesis is severely inhibited when 2% of the red seaweed Asparagopsis is added as a supplement in cows food.
And the effect of bromoform (molecule synthetised in high quantity by the red seaweed Asparagopsis) has shown same results (methanogenesis inhibition) in rumen fermentation of sheep in vivo (Lanigan 1972.

References:
Lanigan G (1972). Metabolism of pyrrolizidine alkaloids in the ovine rumen. IV. Effects of chloral hydrate and halogenated methanes on rumen methanogenesis and alkaloid metabolism in fistulated sheep. Crop Pasture Sci 23:1085–1091

Machado, L., Magnusson, M., Paul, N. A., Kinley, R., de Nys, R., & Tomkins, N. (2016). Identification of bioactives from the red seaweed Asparagopsis taxiformis that promote antimethanogenic activity in vitro. Journal of Applied Phycology, 28(5), 3117–3126.