I guess I should clarify, I am not saying that interracial couples would make up a large PERCENTAGE of the federation population, but rather, due to the federation's large populations, even a small percent of interracial procreation would add up to huge numbers.
Stanford: 7 percent of couples interracial
Factoring in all racial combinations, Stanford University sociologist Michael Rosenfeld calculates that more than 7 percent of America’s 59 million married couples in 2005 were interracial, compared to less than 2 percent in 1970.
Lets say that in the federation's case, the percent is far, far lower, say, actually one tenth of a percent. Even with this a small number, with the huge population of hundreds of billions, the number of hybrids would be in the millions.
Well, let's see.
We know from
Star Trek (2009) that the planet Vulcan had a population of about 6 billion in 2258 in the alternate timeline. As that timeline only diverged from the main timeline in 2233, it's improbable that that was a recent development, so let's assume that Vulcan has had a population of around 6 billion for most of its modern history.
And let's assume that Vulcan, as a founding Federation Member State with a very stoic culture, has a fairly typical population for the capital planet of a Federation Member State. (Member States, let's recall, can encompass themselves more than one planet, the same way a state in the U.S. can encompass more than one landmass -- Michigan, for instance.) So, assume an average of six billion per Member State capital planet -- some have more, some have less, but let's use 6 billion as an average.
We know from
Articles of the Federation that the pre-Borg Invasion Federation had 155 Member States.
155 x 6,000,000,000 = 930,000,000,000. 930 billion.
Now, let's assume every Member State has an average of three other worlds under their jurisdiction. And given the really low populations listed for most colonies, let's assume they usually have an average of 500,000,000 per planet.
500,000,000 x 3 = 1,500,000,000.
1,500,000,000 x 155 = 232,500,000,000. 232.5 billion.
So, 930 billion + 232.5 billion = 1,162,500,000,000.
And let's assume that the Federation government itself has colonies that aren't part of any Member State. Let's assume an average population of 250 million, and let's assume that there are maybe 50 of them.
250,000,000 x 50 = 12,500,000,000.
So, 1,162,500,000,000 + 12,500,000,000 = 1,175,000,000,000.
So a total Federation population of 1.175 trillion.
So, out of that population, let's say 00.1% are in interspecies relationships.
1,175,000,000,000 x 0.003 = 3,525,000,000. So we'd be looking at a Federation with around 3.5 billion interspecies hybrids.
However...
I'm skeptical of the idea that even .1% of the population of any given species would enter romantic relationships with other species. Let's assume that it's actually 00.01%.
1,175,000,000,000 x 0.0001 = 117,500,000. So, we'd be looking at a hybrid population of about 117.5 million hybrids.
And, of course, there would be a question as to how many of these hybrids would be fertile themselves.