Hello, new member here. Just wanted to offer some input.
Well, we have to ask: what the source of anti-Romulan sentiment within the Federation? Yes, the Romulans are secretive, and deceptive, and xenophobic to outsiders, and are always in conflict with the Federation. But the Klingons have also been known to be in conflict with the Federation, and have managed to sign peace accords and remain allies for decades.
Think about it: by the time of ST: Picard, there’s been animosity between the two powers for nearly 250 years!
ENT era: First contact with Romulans in 2152. There was secret Romulan influence of the Vulcan government & their antagonistic relationship of Earth at the time, due to a desire for reunification. The future founders of the Federation unite against a Romulan drone ship and the Romulan attempt to pit them against one another. And a screen cap from In A Mirror Darkly, part 2 from the USS Defiant clearly shows that the Romulan War evolved from Earth forces to a Earth/Vulcan/Andorian/Tellarite alliance.
It is suggested in DS9 that the Romulans reached Earth during the Romulan War, resulting in a devastating attack unmatched until the Dominion do the same. And ST: Beyond suggests that, aside from MACO ships like the Franklin being employed to face the Romulans, the Romulan War was as significant as the Xindi crisis (which was supposed to be the 9/11 of that era). And from what is known about the Xindi crisis, it had an impact on Archer and his crew both emotionally and morally while they searched for the Xindi weapon, and had an impact on Earth with Terra Prime.
Non-canon sources have suggested that the Romulans attacked, hijacked and killed the crew of Earth cargo ships a decade before the launch of the NX-01 under the guise of space piracy, which led to those cargo ships requiring military escorts; attacked Earth’s first starbase under the guise of space piracy, although they were considered the culprits afterwards; the kamikaze attack by a Romulan Bird of Prey on Coridan that killed billions to prevent them from reaching warp 7 and joining the Coalition of Planets according to The Good That Men Do; and a possible attack on a neutral Denobula during the war that killed millions. Although these events have never been made officially canon, they are plausible events to explain why Federation and the Romulans have always been at odds with each other.
TOS era: The first encounter in over a century & first ever official face to face viewing. The history of Romulan War is briefly explained (which is supposed to have involved "primitive atomic weapons") & lingering prejudice because of the war on the Federation side still exist. For about a century, Romulans are considered warlike, cruel & treacherous by the Federation. A Romulan Bird-of-Prey was still carrying nuclear weapons and they choose to self destruct over accepting help from Kirk after their ship is damaged in battle, as it is “the Romulan way.” Later on, the Romulans are briefly allied with the Klingons, and the USS Enterprise is briefly captured by the Romulans.
TNG era: Relations between the two are still frosty, with the Tomed Incident resulting in the Treaty of Algeron; USS Enterprise-C being destroyed by Romulans; the Romulans still considering their loss at the Battle of Cheron humiliating (according to The Defector); being revealed to be a Romulan within the Federation was enough to end careers (as seen in The Drumhead); and there was an attempted reunification with the Vulcans. However, the Federation and the Romulans were capable of working together in various situations (including, but not limited to, the Dominion War), they worked together to defeat Shinzon’s forces, and were supposed to have been working on a joint task force by the end of Nemesis. The relationship between the Federation and the Romulans was thawing, especially post-Dominion War. Its also noted by Data himself that the Romulans rarely attack first with their long history of war. They're mostly defensive.
So, either something happened after the joint task force was formed, or there are still deep-seated resentment from the Romulan War from the 14 member worlds that threatened to leave the Federation. And it is similar to how Japan will acknowledge but not apologize for war crimes involving China and Korea during WW2, and will just focus on memorials for their war dead. Likewise, the Romulans aren’t sorry for their actions before, during, and after the Romulan War, however certain member worlds have grown quite fed up with the lack of apology to the point that they would rather leave the Federation than continue to work with the Romulans.
