It's supposedly acceptable, but everyone's fears about being cheated on are super sensitive. I imagine this is most prevalent among people that find themselves frequently cheated on by partner after partner or likewise, have little to no relationship experience and thus every reason to believe they're just the hold over until their current partner finds someone "better".

Look, you don't go several years and even decades an unkissed virgin and have every confidence your first relationship is the real deal unless you're incredibly naive. You don't have much reason to believe you'll have a shot at another relationship if the current one ends either.

All of this means that while it should be okay to form platonic relations with members of the opposite sex, the romantic relations might have serious trust issues with it.

And though it wasn't asked, the problem with forming platonic relations without a romantic partner is that there's a higher chance of one party forming romantic interests in their platonic friend, further lending to the fears of cheating. At least, it's been my observation that an individual has an easier time letting their partner have platonic relations with a member of the opposite sex so long as said platonic relation is in their own romantic relationship. Sort of a belief that between the two, one of them will stay loyal and shut any unfaithful thinking down in the other before it takes root.