It's a good question and I honestly haven't got a concrete answer. Liveries changed from time to time, so a livery in 1450 might not be the same as in 1485. Percy and Neville troops served alongside each other (relatively speaking) on the Northern Marches, so a joint colour scheme might have been really useful. The key protagonist in the Percy-Neville dispute was Lord Egremont, who was a Percy younger son and who might not have used Black/Red. The Nevilles also seem to have used Red/Black, as evidenced by the garter stall plates of Montagu and iirc Salisbury, which are usually on the money.
You're not the only one wondering about this btw
Link.
Other famous feuds you might like include; Pastons versus the Duke of Norfolk, Lord Berkeley versus Viscount Lisle, Earl of Devon versus Lord Bonneville and Kynastons versus Stranges. The Duke of Buckingham was involved in one with someone whose name has slipped mind too. AFAIK these all used different liveries, so the colour problem shouldn't arise.
Alternatively paint one lot Red/Black and the others Black/Red