I don't know that this is really controversial - it's pretty obvious - but: Trek was created by Hollywood liberals who absolutely intended the messages of the show to be progressive as they understood such things. Trying to find support for conservative positions in it is a misreading of the intent of almost everyone who did creative work on it.
TIC

TOS
Values change, todays conservative might find a future where mainly American white humans rule a United Earth and are highly influential in a fictional galactic organisation not a bother
TNG
The few female admirals/captain in the show was probably tolerable for a modern conservative after all , Sarah Payne is a conservative and she wanted to be VP
DS9
Black male boss - Might be slightly disturbing
VOY
Female captain and engineer - might be slightly disturbing
ENT
A conservative dream?
PIC
Barely Tolerable? Female admiral, swearing, great white male hope not so great?
DISC
A conservative nightmare....