In the beginning it would probably depend on who caught the driver in question. The specialist press are ultra-cautious when reporting off-track negative stuff, partly because they tend to respect the people involved in F1 more than the general press, partly because they are used to morality not exactly being the highest priority in F1 and partly because bad publicity for a driver tends to mean bad publicity in F1. Unless the driver did something which was flat impossible to hide from the public, the cheated party was a F1 paddock member with an independent communication mechanism and the job security/confidence to use it or the driver makes a public statement on the subject, an incident of cheating not seen by the general press or one of their sources would almost certainly not get reported at all. It might make the gossip circuit within the F1 media centre but no further than that (people who can’t keep a secret don’t get to stay in the media centre gossip circuit long).
If one of the tabloids got hold of the story, my first thought would be to wait for clarification. I’ve seen so many stories from tabloids that were either false or seriously misinterpreted key information that it would be foolish to change my opinion of a driver on what could be journalistic or editorial licence. Wouldn’t be the first time a bodyguard has been mistaken for a friend…
Assuming that there was subsequent, reasonably reliable confirmation that a F1 driver had cheated on their spouse might make a difference in my opinion of them depending on how much I knew about them beforehand. I’d certainly feel sympathetic towards the driver’s spouse because it’s always unpleasant to be cheated upon, but not every incident of cheating is created equal. Often in such a relationship (at least in the world at large) the cheating partner meant to make the relationship with their spouse work but either didn’t grasp the true meaning of fidelity (not everyone agrees on what constitutes “cheating”) or is cheating as a symptom of other problems with the relationship (frequently as simple as the couple not communicating well enough about day-to-day problems). Granted that cheating is always a bad thing to do, but a mistake made in ignorance or incompetence in maintaining the relationship isn’t as bad as the same mistake wilfully made for greed or with deliberate intent to hurt. Some people are better at creating and maintaining monogamous relationships than others, and while you’d hope the ones that are bad at maintaining monogamous relationships avoid getting married, it doesn’t always happen – in the world at large or among those who are in the limelight. F1 drivers might have to be pretty intelligent to get into the series but nothing in the entry requirements obliges them to have high interpersonal wisdom.
Bearing this in mind, I find it difficult to get upset at a driver who’s cheated on their partner unless that driver had previously led me to expect they wouldn’t. It’s particularly difficult to get upset when, for the most part, I don’t know anything about F1 driver spouses beyond their names (and I’m not confident I could even name all the current ones). With that little information, there’s only really what the driver has said on the subject, plus anything reasonably reputable sources have observed, to make a judgement.
That said, there are maybe five F1 drivers who would seriously surprise me if they were caught cheating from the information I’ve heard about them and I’d be pretty upset if they cheated. That said, I’d be more interested in what they did in response to being caught cheating than the act itself. If they tried to make amends (either by repairing that relationship or refraining from cheating again) then I wouldn’t be upset with them for long, for character development is an important part of being human and something I find makes drivers more likeable. If they kept repeating the error of cheating on their partners (I don’t mean by becoming a playboy, since they tend to be open about their intentions and thus aren’t cheating), on the other hand, my patience would be tested. For that matter, I would also start wondering if it would have an effect on their driving. It’s not just a question of the emotional turmoil but the inability to learn how to maintain one (romantic) relationship could point to difficulty maintaining the (colleague/friend) relationships needed to get the maximum out of a racing team. In that sense, the way a driver lives their personal life could give clues as to how they do their job – though this does not justify the senseless and immoral things many tabloids do to get lowest-common-denominator stories…