The Physical characteristics of a half roman half german child must have been very noticeable.

Why must we presume that? In the U.S. alone there are millions of children born from, say, Italian and German parents, and I've never met anyone who can instantly tell that a child with one German and one Italian parent apart. What features would be noticeable with a mix of such closely-related peoples? I'm including for the Romans here as well, since I can't think of any features that Germanic peoples are described as having in antiquity that weren't at least known in Mediterranean individuals, although sometimes they were rare. Besides, it's not as though all Germans looked like that--undoubtedly, then as today, the vast majority of people looked more or less the same.

In any case, we have lots of cases of children from different ethnic groups in antiquity, and no records whatsoever of discrimination against them on the basis of their parentage. Themistocles, for example, was the son of an Athenian father and a Thracian mother, and the only insult he ever received about his parentage was the accusation that his mother was a vegetable-seller in the agora, a common accusation that's kind of like saying your mother was a scullery-maid. The closest example to anything like such discrimination is Cicero's accusation that Piso was the descendant of a Syrian slave. Cicero's accusation is pretty demonstrably false, and it doesn't make sense since he changes the ethnicity of Piso's supposed servile ancestor from Syrian to Gallic at will, purely for humorous effect (and to make fun of Piso's supposedly ruddy complexion--it appears Piso got red in the face easily, as well he might, sitting for nearly four hours listening to Cicero tell obvious lies about him). But it's notable that even here Cicero is dwelling not on accusations that he's of mixed race, but that one of his ancestors was a slave--where the slave came from doesn't matter, the point of the joke is that it's a slave