We all know that Starfleet officers follow the Prime Directive but are they duty bound to stop other races from interfering in other civilizations? If not, then what stops someone like the Cardassians or the Romulans from taking over pre-warp civilizations?
Starfleet General Order 1 applies ONLY to Starfleet. The Prime directive does not apply universally inside of Federation space, nor are non-Starfleet officers and non-Federation officials expected to uphold it. The Federation cannot enforce this even against its own citizenry, if the citizen is not acting as an agent of the government. To quote Memory Alpha (emphasis mine):
The fundamental principles were an important part of Earth Starfleet procedures as early as 2152, but it did not go into effect as a General Order until sometime after 2168. (ENT: "The Communicator"; TOS: "A Piece of the Action") The directive remained in effect well into the 24th century and applied to at least Starfleet and Merchant Marine personnel, but specifically did not apply to ordinary Federation citizens. (TOS: "Bread and Circuses"; TNG: "Angel One")
Again, the Prime Directive is Starfleet General Order 1. The Federation cannot even fully apply it to itself, let alone other nation-states.
To extend this to answer the question as asked; A Starfleet officer cannot themselves interfere in the inner workings of another society or make contact with non-warp capable races. They cannot prevent non-officers from doing so, nor can they really do anything about it when one nation-state does so against another. Also, the nation-states you specifically mention have done what you asked about.
The Federation claims political sovereignty over a three-dimensional slice of the galaxy. Within this domain, they do not allow any encroachment by foreign powers, either on planets or just floating in space. While there is some allowance for overlap with truly alien beings who do not require the same environment as humanoid species, in general if you're "in federation space" you wind up constrained by all the rules of the federation, as you either joined the federation or are there are their sufferance.
Outside of federation territory, this outlook is not shared by all space faring races. The Ferengi, for example, actually held out the Prime Directive as proof that the Fedreation were barbarians when arguing with the last guardian of the Tkon, as they denied lesser species access to their technology (and thus denied themselves their profit.)
I think the best evidence that this can happen is that the Son'a went through the whole song and dance of hidden observation of the Ba'ku, despite not caring much for it, and presumably this was a condition of their partnership with the Federation.
Of course, in reality, the Prime Directive was about to be broken in a rather fundamental fashion by both parties, but this was a concealed, clandestine activity and cannot be deemed to represent any sort of legitimate Federation policy.
Note that the planet Ba'ku lies within Federation space, so Insurrection doesn't tell us whether the Federation would (or would be able to) impose the same conditions on missions outside of their territory.
The concept of "Federation Space" leads one to think in planetary terms. When something or someone, is outside of federation space, they may be separated from interaction by months or years of travel. Space is huge, and no political entity could ever police all of it. The 'Prime Directive' seems to apply to Starfleet and its personnel, with those outside of it, even federation citizens, not particularly concerned with it. One sees many violations of the rule in various episodes, but usually the most flagrant are those by non-federation or at least non-starfleet persons. In the original series, a highly advanced race took it upon themselves to end a war between two lesser species simply because the violence expressed by these unevolved beings was painful to them. This translates to a violation of the prime directive on their part, even though the races in question had warp technology. I suspect that in the Star Trek universe there are more than a few lawyers who make a good living off of the 'prime directive'. Insofar as imposing it on other civilizations/races the federation has more than enough trouble enforcing it among their own citizens, without reaching out to others.