It all comes down to how much reactivity will the Origin characters get and that we just don't know yet. Will Shadowheart get additional dialogue choices over a Tav cleric of Shar? Will Gale be able to get more than a Tav wizard?

Probably, but how much and will it truly make a difference? Unknown at this point of time.

In terms of content I don't think we will be locked out of anything playing a Tav.