I wonder why noone has mentioned M'Khiin. She is a true neutral goblin shaman and left her tribe, because she was more mature than her kinsmen. She likely wanted to make more of herself. So this is your precedence in the Baldur's Gate lore. That was a rare thing 100 years ago, just like a good Drow. Drow seem accepted now for the most part, as are Tieflings. A goblin as a companion is not far-fetched and would therefore also work as an Origin character. I do not know about the custom PC. I do wonder why they haven't added a goblin companion yet. I'd wager there are more engine reasons behind it. You would have to remodel armours for this one little fellow, as they have a different posture than dwarfes, halflings and gnomes.

In any case you can be sure that noone in the world, at the current state, would bat an eyelid over a goblin, When neither even Githyanki or Drow are a problem. The culture seems extremely liberal in all other regards, too and the reasoning behind it boils down to 100 years having passed.

So, yeah, engine reasons. Hence no Lizardmen either or whatever other exotic shape races there are. In the current game not having an upright posture is what keeps you from getting added I would say.