Short answer, RAW says yes but most DMs would houserule against it.
According to the RAW on page 173/174 of the PHB, adding half your proficiency bonus is still adding your proficiency bonus. You can add your proficiency bonus only once and multiply or divide that bonus only once, but adding half your proficiency is still adding your proficiency, so Reliable Talent does stack with Jack of all Trades/Remarkable Athlete according to the RAW.
Conversely, the RAW disallows Jack of all Trades to stack with Remarkable Athlete. I think this is the wrong way around. Jack of all Trades with Reliable Talent is overpowered (never roll below a 10+2 from JoaT on any ability check at level 13?) whereas Jack of all Trades with Remarkable Athlete is decidedly underpowered (gain proficiency in up to 4 skills at level 5 instead of having Extra Attack or 3rd-level spells, bearing in mind you probably already had half your proficiency in all skills at level 2, making this bonus next to useless).