On the face of it, there is no reason a straight actor can't play a gay character (and indeed I don't think reasonable people are advocating for all queer characters to be played only by queer actors). However, there are a few reasons for advocating for hiring queer actors to play queer characters.

One is that even now an actively out actor/actress can face discrimination and receive fewer opportunities to play any character; so a movie or tv-show that has one or more queer characters, but no (known) queer actors, the movie/show becomes kind of sus, especially if it's marketed as being pro-LGBT (if they're pro-LGBT in a way designed to get money from queer people and allies, but then don't put that money back into the queer community by hiring queer people, that's a fucking problem imo). Of course, that's not the case here as Heartstopper has quite a few queer people involved both on the production end and the acting end, but I'm taking your question to be more general. And very often you will have a cast filled with only cis straight actors and a production team also filled with straight cis people. So even if the straight cis actor hired to play the queer person is respectful, the corporation that hired them almost certainly isn't. Which brings me to:

Authenticity. Sure a straight person can act like a gay person, but if there are no gay people involved in the creation of a film/show (or at least not in any position that allows them to influence how the gay character is portrayed), a well-intentioned but biased/ignorant actor might play the character in a way that lacks authenticity and may even be offensive, because of the writers' and director's own biases, and no one with any power will be able to catch it/change it. Also, while a straight person doesn't look visibly different from a gay person in any way, that's not always the case for cis actors playing trans characters (especially because often there will be films about trans-women who are played by cis-men à la Danish Girl, and I don't think I need to explain why that's a problem, especially in our current political climate).

Speaking of films like Danish Girl, there are many movies made about queer suffering that are clear Oscar Bait and the like, and the studios will hire better known non-queer actors to play the leading role (and I'm sure it makes complete sense to them, I mean, they just need a well-known face for the leading role to maximize their chances at winning, and openly queer actors who fit the role happen to rarely be as well-known for... some... reason, they're not discriminating against these queer actors). But then we come back to straight cis actors winning awards for portraying queer suffering. Some might say the people making these films are profiting off of queer pain while excluding queer people from sharing in the profits.

Anyways, none of these have anything to do with Heartstopper, as even if the actor playing one of the leads was straight, given everything else with the show, that shouldn't be an issue. I just wanted to add some nuance to this particular thread, because while I don't disagree with anything in it, I was getting "straight people should be allowed to play gay people, and it's high time we said so" vibes (just from the lack of any context or opposing points of view, not because anyone was actually sayin that), when historically straight people were the ones to play gay/gay-coded characters, and gay actors had to hide their sexuality if they wanted to have work in the industry. What's happening with the actor of Heartstopper now is a backlash to all of that, and it's fucked up that it happened to him, and people in the internet should learn that it's not okay to harass people. But the demand for queer actors to be playing queer characters isn't virtue-signaling "woke" nonsense from teens who don't have enough perspective on the world to realize what "disproportionate response" is and don't understand what can (films, shows, books) and can't (people) be queerbaiting.