Tormyr I liked your post.
Starting with the Ripper class,
I actually gave it more attacks because by using only his natural weapons he will be doing WAY less damage than a barbarian with a 2d6 great sword. The extra attack is meant to make up for the fact that he will not only be doing less base weapon damage but the odds of a claw fighter getting magic claws is a lot less than a magical great sword.
As for your racial changes I agree with you except for one thing. The adv vs poisons and disease was meant to represent the fact that a Gnoll eats everything and thus would be more resistant to posions and diseases. Perhaps a feat for this trait
While the gnoll has *ahem* questionable culinary habits, none of the gnolls in the MM or Volo's have this feature. That being said, my version was sparse on racial features. So this could easily be added. It would also work as a more limited version which only covers disease and poison that is ingested.
When comparing features on an exotic/homebrew race or class that has something fairly unique, I usually consider that uniqueness to cover some portion of any mechanical shortfall. I would also suggest just having the damage for the Bite and Claw attacks scale all the time and not require raging. As for the comparison of damage, the Berserker vs. Flesh Ripper looks something like this:
Berserker with greatsword
Level 1: 10 (2d6 + 3)
Level 3: 10 (2d6 + 3) sometimes an additional 10 if taking a point of exhaustion
Level 4: 11 (2d6 + 4) sometimes an additional 11 if taking a point of exhaustion
Level 5: 22 ((2d6 + 4) * 2) sometimes an additional 11 if taking a point of exhaustion
Level 8: 24 ((2d6 + 5) * 2) sometimes an additional 12 if taking a point of exhaustion
Original Flesh Ripper (only using natural attacks and no boosting natural weapon attacks from raging)
Level 1: Club 5 (1d4 + 3) sometimes additional 5 from from Rampage
Level 3: Claw 5 (1d4 + 3), bonus attack Claws and Bite 8 (1d4 * 2 + 1d6) for a total of 13
Level 4: Claw 6 (1d4 + 4), bonus attack Claws and Bite 8 (1d4 * 2 + 1d6) for a total of 14
Level 5: Claw 13 ((1d4 + 4) * 2), bonus attack Claws and Bite 8 (1d4 * 2 + 1d6) for a total of 21
Level 8: Claw 15 ((1d4 + 5) * 2), bonus attack Claws and Bite 8 (1d4 * 2 + 1d6) for a total of 23
Original Flesh Ripper (only using natural attacks and boosting natural weapon attacks from raging)
Level 1: 5 (1d4 + 3) sometimes additional 5 from from Rampage
Level 3: Claw 5 (1d4 + 3), bonus attack Claws and Bite 8 (1d4 * 2 + 1d6)) for a total of 13
Level 4: Claw 6 (1d4 + 4), bonus attack Claws and Bite 8 (1d4 * 2 + 1d6) for a total of 14
Level 5: Claw 15 ((1d6 + 4) * 2), bonus attack Claws and Bite 11 (1d6 * 2 + 1d8) for a total of 26
Level 8: Claw 17 ((1d6 + 5) * 2), bonus attack Claws and Bite 11 (1d6 * 2 + 1d8) for a total of 28
Level 11: Claw 19 ((1d8 + 5) * 2), bonus attack Claws and Bite 14 (1d8 * 2 + 1d10) for a total of 33
Level 17: Claw 21 ((1d10 + 5) * 2), bonus attack Claws and Bite 17 (1d10 * 2 + 1d12) for a total of 38
Looking at it slightly differently
Berserker; B with Frenzy;; Flesh Ripper; FR raging;; FR with Rampage; FR raging Rampage
Level 1: 10; N/A;; 5; 5;; 10; 10
Level 3: 10; 20;; 13; 13;; 11; 11
Level 4: 11; 22;; 14; 14;; 13; 13
Level 5: 22; 33;; 21; 26;; 18; 19
Level 8: 24; 36;; 23; 28;; 20; 21
Level 11: 24; 36;; 23; 33;; 20; 22
Level 17: 24; 36;; 23; 38;; 20; 23
The original Flesh Ripper keeps up with the Berserker with a greatsword just fine when neither are raging. When raging, the Flesh ripper consistently gets the damage the berserker can get without the need to take a point of exhaustion. This also removes the point of Rampage, as 3 attacks with no ability modifiers will always be as good or better than the one Bite from Rampage. The Flesh Ripper taking the off hand bonus attacks is as good or better than a Flesh Ripper raging and using Rampage.
Suggested Flesh Ripper (bonus attacks from raging)
Level 1: Club 5 (1d4 + 3) sometimes additional 5 from from Rampage
Level 3: Claw 5 (1d4 + 3), bonus attack Bite 2 (1d4) for a total of 7
Level 4: Claw 6 (1d4 + 4), bonus attack Bite 2 (1d4) for a total of 8
Level 5: Claw 15 ((1d6 + 4) * 2), bonus attack Bite 3 (1d6) for a total of 18
Level 8: Claw 17 ((1d6 + 5) * 2), bonus attack Bite 3 (1d6) for a total of 20
Level 11: Claw 19 ((1d8 + 5) * 2), bonus attack Bite 4 (1d8) for a total of 23
Level 17: Claw 21 ((1d10 + 5) * 2), bonus attack Bite 5 (1d10) for a total of 26
Each of those damage totals can be boosted by 3 to 5 if Rampage can be used rather than the bonus attack from raging. So the suggested Flesh Ripper would average 5 fewer points of damage across all levels when not raging and without Rampage. This goes away if rampage can be used, and the Flesh Ripper with Rampage actually pulls slightly ahead at higher levels (25 vs Berserker's 24 at level 8).
Even now the suggested Flesh Ripper can get its bonus attacks much more often when raging as it does not cost a point of exhaustion. In this case, the deficit is only 3-4 points of damage through level 8, and the Flesh Ripper pulls ahead at Level 17 (26 vs Berserker's 24).
Looking at the Berserker vs. the suggested Flesh Ripper
Berserker; B with Frenzy;; Flesh Ripper; FR raging; FR with Rampage
Level 1: 10; N/A;; 5; 5; 10
Level 3: 10; 20;; 5; 7; 10
Level 4: 11; 22;; 6; 8; 12
Level 5: 22; 33;; 15; 18; 22
Level 8: 24; 36;; 17; 20; 25
Level 11: 24; 36;; 19; 23; 28
Level 17: 24; 36;; 21; 26; 31
In this version, the Berserker does a little better, but the Flesh Ripper usually can take a bonus action through either raging or Rampage. This version is simpler to run as the damage die stays the same between the Bite and Claw attacks and whether or not you are raging. Rampage also actually has a use in this build. The Berserker is still the damage king when it uses Frenzy, but that comes at a steep price.
As for the Flesh Ripper not getting magic weapons, this would be a good time to crib the Level 6 magic weapon feature from the monk. It could replace either the current Level 6 or Level 10 Flesh Ripper feature.
So what adventure are you in that a gnoll PC actually works?