Hilariously enough, that's exactly the position of one of the most orthodox branches of Tyr's church in-universe. But they have this position precisely because there are some more liberal temples that allow the mixing of the cleric and paladin or paladin and monk traditions, so it's obviously possible. Really, it all has to do with whether his church and sect tell him that he may not do it, and for a divine caster in the Realms, that does matter very much.