Seaweed

Carrots and parsnips fork when the root hits an obstruction. It could be a stone or a lump of manure but manure itself does not cause forking. If you gather seaweed then dry it out completely it can be crushed down almost to a powder and applied either as a base or top dressing. I normally use it as a liquid feed and then compost it but I've tried it in all sorts of combinations and wouldn't be without it. Thank goodness I live by the sea.

Too risky using farmyard manure unless you can be absolutely certain it contains no herbicide residues. I've found that seaweed, while it may not be high in major nutrients, has a lot of other stuff which seems to be very beneficial to soil and plant health.

manure itself does not cause forking.

Although high levels of Nitrogen also causes forking, and some Manure is rich in Nitrogen (particularly urine-rich manure, for example from cattle overwinter bedding, and Chicken manure).