What do we do if SETI is successful?

For a somber, deeply intellectual view of what could happen, I can't recommend enough Stanislaw Lem's His Master's Voice: https://en.wikipedia.org/wiki/His_Master%27s_Voice_%28novel%...

"Given that our civilization is unable to assimilate well even those concepts that originate in human heads when they appear outside its main current, although the creators of those concepts are, after all, children of the same age—how could we have assumed that we would be capable of understanding a civilization totally unlike ours, if it addressed us across the cosmic gulf?"

Me and my dog cannot talk.

I understand my dog and he understands me.

If they experience death then we have massive common ground already.

Humans and dogs have evolved together to be cooperative…

would you feel common ground with a predatory fish? Or a plant? An insect colony?

  > would you feel common ground with a predatory fish? Or a plant? An insect colony?

Yes.

Humans famously show compassion for all of these. I don't think alligators co-evolved with Steve Irwin.

Humans even show compassion for rocks and non-living things. We show compassion for the literal ground. We anthropomorphize it. Is this anthropomorphization not an attempt to understand and have compassion.

Regardless, you just asked how OP feels. I don't know how they do, but I can say how I do. "Yes"

>> would you feel common ground with a predatory fish? Or a plant? An insect colony?

> Yes.

> Humans famously show compassion for all of these.

But alligators rarely show compassion for humans, barracudas are not known for saving drowning babies and plants frequently show no compassion to anything.

IOW, Alien life might resemble alligator mindsets more than human ones. We don't know.

> But alligators rarely show compassion for humans, barracudas are not known for saving drowning babies and plants frequently show no compassion to anything.

On the other hand, even predatory mammals are documented on occasion to render aid to humans (i.e. dolphins rescuing humans from drowning, or intervening in shark attacks), and in domestic settings can be convinced to raise young from other species (domestic cats/dogs will raise most baby animals if introduced correctly). It's not as cut and dried as a hard species boundary on compassion.