So a regiment for a game I am in, has...

Regiment: Drop Troop (gives lascarbine and guard flak)

I get that the laspistol and flak pistol are replaced (the rules spell it out)

Training Doctrine: Close Quarter Battle (gives light carapace and a compact lascarbine)

So what happens next? I assume that the lascarbine and guard flak gets replaced, but are the regiment points spent on the drop troop gear wasted?

i would let the characters choose from all avaible options
makes for more diverse characters as well

some characters might not be strong enough to wear a carapce without penalty for example

the compact lascarbine is slightly weaker but has other benifits

The errata actually answers something very close to this in its FAQ section:

Question: If a regiment is created with two or more options that
replace its Main Weapon, which one applies as its Main Weapon?
Answer: Those involved in creating the regiment (presumably,
the players and the Game Master) choose which one becomes
the regiment’s Main Weapon.

So for the regiment you're talking about, the players and GM should discuss which one to go with.

Thanks, too bad the regiment points got "wasted" though