hogoneko to senzyuuneko ha aisyou ga ii.

A common reading is:

ほごねこ と せんじゅうねこ は あいしょう が いい。
Hogo neko to senjū neko wa aishō ga ii.

Breakdown:

• 保護猫（ほごねこ） = rescue cat / adopted cat from a shelter or rescue
• 先住猫（せんじゅうねこ） = the cat already living in the home
• 相性（あいしょう） = compatibility
• いい = good

保護猫 literally means a protected/rescued cat.

In real-life usage, it usually refers to:

• a rescue cat
• a cat taken in from a shelter
• a cat that has been saved and rehomed

So it is not just any pet cat. It specifically suggests a cat that was rescued or adopted through some kind of protection effort.

Not exactly. 先住猫 means the cat that was already there first.

It is often used when introducing a new cat into a home. So:

• 先住猫 = resident cat / existing household cat
• 保護猫 = newly adopted rescue cat

The word 先住 has the idea of already living there beforehand.

Here, と means and.

So:

• 保護猫 と 先住猫 = the rescue cat and the resident cat

It links the two nouns together as a pair. In this sentence, the speaker is talking about the compatibility between those two cats.

This is a very common Japanese pattern.

• 保護猫と先住猫は = as for the rescue cat and the resident cat
• 相性がいい = the compatibility is good

So は marks the topic, and が marks the thing that is specifically described by いい.

A natural way to understand the structure is:

• Topic: the rescue cat and the resident cat
• Comment about that topic: their compatibility is good

This kind of X は Y が いい pattern is extremely common in Japanese.

Because いい is an adjective, not an action verb.

Japanese adjectives often describe a noun marked by が:

• 相性がいい = compatibility is good
• 天気がいい = the weather is good
• 頭がいい = smart, literally the head is good

If you used を, it would sound wrong here because を usually marks the direct object of a verb.

Because いい can already function as the predicate by itself.

This sentence is in a plain style:

• 相性がいい。

A more polite version would be:

• 保護猫と先住猫は相性がいいです。

You do not add だ after an い-adjective like いい.

So:

• correct: いい
• correct: いいです
• incorrect: いいだ

Yes, this is a small irregularity.

Historically, the word is よい, and that form still appears in some situations. But in everyday speech, いい is much more common.

Examples:

• いい = good
• よくない = not good
• よかった = was good

So the forms mix:

• present casual: usually いい
• negative/past forms: usually based on よい

That is normal and something learners just have to get used to.

It can suggest both, depending on context.

Literally, 相性がいい means:

• to be compatible
• to be a good match

For pets, people often use it in situations where English might say:

• They get along well
• They’re compatible
• They seem to be a good match

So it does not only describe personality in an abstract way. It can also refer to whether two animals live together smoothly.

Yes, absolutely.

That version means:

• The rescue cat is compatible with the resident cat.

Compare the nuance:

• 保護猫と先住猫は相性がいい。
  Focuses on the pair together.

• 保護猫は先住猫と相性がいい。
  Focuses more on the rescue cat, and says it is compatible with the resident cat.

Both are natural. The original sentence sounds a bit more balanced, as if looking at the relationship between the two cats as a pair.

By itself, it could be understood either way, depending on context.

It might mean:

• This rescue cat and the resident cat are compatible.
• or more generally, in a certain situation, the rescue cat and the resident cat get along well.

Japanese often leaves out things like:

• the
• this
• my
• our

So context tells you whether the speaker means a specific pair of cats or is speaking more generally about a known situation.

Japanese often leaves that kind of relationship unstated when it is obvious.

In English, we might say:

• Their compatibility is good

In Japanese, once 保護猫と先住猫 has already been mentioned, 相性 naturally gets understood as the compatibility between them.

So Japanese does not need a separate word like their here. The connection is understood from context.