Unfortunately, that isn't always true. Hotels have public perception that they have to deal with as well. It doesn't matter how well behaved you may be on their property, if it would be bad PR for them to host you because you're considered a convention for sexual deviants and child molesters...well...they aren't going to host you. They figure that they'll lose less revenue from cancelling your reservation than they would from people boycotting the hotel for "supporting sick freaks". You see.
And the media cares about whatever sells newspapers or online subscriptions or provides viewership to their networks. If it's controversial, it'll sell.
It absolutely can happen. It's a judgement call made on the part of the business. If the business decides they're willing to risk the negative press, they'll keep the booking. If they decide it's bad for business, they'll cancel it. It's just the way it works.
As for restaurants, it's rare for people to be refused service, but most restaurants to reserve the right to refuse service to anyone. Again, it comes down to a judgement call: is it worth it refuse service? Most people would focus on the host of the convention, not necessarily the restaurants serving food to whomever.
