Actually, this might introduce a new form of racial tension between humans and asari because there will no doubt be pressure to keep the human race going. You might have political leaders and human groups on the Ark voicing disapproval at other humans choosing to have asari children. Unlike humans, asari never have to worry about their numbers dwindling. They can live to be a 1000 years old or more, can mate with anyone and still produce asari children and we don't know how many children a typical asari has in that long lifetime.
This trip will no doubt intensify the "earth first" mentality in some humans and the asari, for the first time, might actually be considered a threat to them. The last thing they would want is to "help" increase the population of another species over their own. I always found it astonishing that there wasn't more ill-informed opinions or superstitions about the asari like the other species. They can read minds and memories and can copy the genetic information of others! You would definitely have humans and other aliens accusing them of mind control or manipulating others to get where they are even though it's not actually true. The races will have an unspoken understanding that once they start to branch out in Andromeda they won't be on equal footing forever. Who's going to establish the most colonies? Who's going to have the most numbers and power in this new galaxy? I like the asari but they need to have more realistic conflicts with other races, not more trivial insults about them stripping.