It is not a must for an orthodox Sri Vaishnava who strictly follows the ritualistic practises to accept the prasadam from a non Srivaishnava devotee. As their strict ritualistic practise are nothing but Bhagavad Thiru Aradhanam, they will not do something that causes hinderance to their worship. It is not a sin if one rejects it.
Notes:
There are two matters that are to be considered – one is austerities and the other is the devotion. It is considered superior to accept the prasadam that are offered to Perumal by the devotees with utmost devotion.
True devotees will not cause hinderance to an orthrodox Srivaishnava, as they are aware of their strict adherence to rituals; hence they will stay away and will not distribute their prasadam to such people.