Are pets with red stats worth keeping? What is the negative modifier doing to the affected stat? 

Just red stats doesn't mean a pet is bad. Naturally people are looking to breed for good genes (so green stats), but just because a pet has a dominant "bad" gene, doesn't mean it's recessive gene won't be great.

Look at this guy for example: http://beastkeeper.com/pet/29566

If you just look at his stats, he isn't worth anything, since he has no green and 2 red stats. BUT if you check out his genetics, you will see that he has quite a few nice recessive genes. Now if you were to breed him to a nice female, his offspring might look totally different! His offspring could inherit Massive Beak, Massive Wings, Steel Muscles and Electric Gland, but just by his red stats, you would never imagine it.

As for your second question, it depends on the gene how it affects the stat. If you hover over a stat, it will tell you how it's affected. If you look at my Rezgod up there again, you will see that his Courage right now is 21. When you hover over that you will see it's actually 42  - 21, because he has the Faint-Hearted gene, which always lowers his Courage by 50%. He is also Slow-Minded, which will always lower his Intelligence by 25% (if you hover on his Int again, you will see it's 63-16=47).

I hope this answered your question - if you mean something else, please elaborate what exactly you would like to know.

Also genes like light bones have both a good and bad modifier. I feel generally this stat is a good one. Its important to know which genes are modifying what. Some may be more harmful or not depending on your goals and wishes. Ultimately the decision is up to you. If you're going by market it depends on the consumer. Some people want only green or black- and some only care about genes or lineages.

I see. Thanks to both of you :)