I'm about five hours in and really loving it, but I'm not sure, like the title says, how important Social Link bonuses are when fusing to unlock new Personas. 
 
For example, I currently have the ability to upgrade my Nekomata Persona to Omoikane, Forneus, or Alp. However, when I proceed to upgrade to any of those choices, I get a warning that I haven't yet established a Social Link that corresponds to the new Persona. Should I wait until I gain the correct Social Link to upgrade to these Personas to get the bonus, or would I be better off going ahead on with the upgrade to strengthen my character sooner rather than later? Since I'm still early in the game, I think I've only opened up three or four Social Links.

You have to adjust with the shadows you are currently encountering,or adjust with the overall squad balance. If Junpei has Agi, and Yukari Garu, a Persona with Zio or Bufu (inherited from their parental Personas or natural ability from the get-go) can complement them, with or without S-Link boost  . A Persona that can absorb electricity is a Persona that can absorb electricity, with or without S-Link boost.

You can upgrade if you want. You might not even see some of the links for a bit. What I do is if the persona seems really good (regardless of my social link status) then I make it and pull out any of the ones I used that I still want.