Wow, 24 pages arguing (debating?) about this question!
My answer comes in two flavors, which only exacerbates the OP's situation.
1) It is way cooler for the Tabaxi player to have 45' movement left, instead of 30'. Let the player be cool.
2) Somewhere in the 5e ruleset I read something about "different movement speeds apply to each other". I.e. if you have a move speed of 30', and a fly speed of 60', but you need to run 10' out of the tunnel before you can fly... you only have 40' of fly speed left.
#1 is simple, easy, cool, and matches what the Rogue can do with Cunning Action. Therefore, if pushed, I will decide #1.
#2 is math-ier, and more consistent... the Tabaxi is increasing its base speed, yada yada, 24 pages of this math = 30' remaining.
As the DM, #1.
Now, something I've learned in 35 years of making "clear and obvious decisions"... check with your players! Not "do you want your character's cool ability to work like this?"... of course they do! Instead, the question is "Is this the way this and similar abilities should work... for you... and all your opponents?" Not surprisingly, there are no peasant railguns in my campaign, or coffeelocks, or or or. Even "crunchier crits" (max + roll) was approved by a narrow margin.
[P.S. I asked my table. The tabaxi gets 45', because the rogue players didn't want to see curtailment of their speed, and they weren't worried about the rare speedster opponent.]
Tangentially, I arbitrarily ruled that combat-based speed bonuses do NOT translate to "normal" movement. Rogue PCs do not naturally move 50% faster than all other classes. To (mis)quote a certain movie dwarf: "We [rogues] are natural sprinters! Very dangerous over short distances... we're wasted on long-distance." If your Base Speed is changed, it changes your long-distance speed; if you have an ability that grants extra movement (Tabaxi Feline Agility applies here too)... that doesn't change your base speed, and does not apply.