Reason to create more than one Sector in Stellaris

So there are different methods of increasing relations with other empires:

• Establish an embassy: you can establish an embassy with the other empire in the same screen as the screen shot you provided. This will increase relations slowly until it reaches 100. You have a limit of 3 embassy by default but government type options can allow you extras.
• Rival the same empire: If the other empire has a rival, rivaling that empire will boost your relations by 25 ⁽¹⁾; this only lasts for the duration of the rivalry.
• Select xenophile traits: being a xenophile will increase other empire relations by 10, or by 20 if fanatic xenophile.

(1) Diplomacy - Stellaris Wiki: Opinion modifiers » Mutual rivals (17 May 2016)

You can't get rid of the differing war philosophy penalty, because that is based on your empire ethics. Instead, you need to get enough bonuses to offset the penalty.

I'd have to do some testing to ensure that this is the case, but here are some things that I believe would help:

• Increase their opinion of you. You're already getting a +21 bonus. There should still be some levels higher than that, though.

• Some things, like a Non-Aggression Pact, will help not only your opinion, but give a direct buff to the Alliance negotiations. I think Migration Access may help in this way as well. You may not be able to get migration access, depending on your mutual ethics, but one-way is probably better than neither.

• You don't appear to be trading with the empire. Trading improves their opinion of you by +5, and may directly impact the alliance negotiations. I often just trade a few minerals a month for a few energy a month.

• Common rivals improve relations. Determine who their rival is from the Empire Contacts screen, and declare the same rival.

• Common threats improve relations. If they're at war with somebody, go to war with them as well.

• If you become significantly more powerful, you can increase the "relative power of empires" modifier.