Do you use an antifungal spray?

No. Should I?

Its a rite of passage.

If that is powdery mildew, there are commercial and home made sprays.

Looks like it. Take a few aspirin and a gallon of water and call us next week.

I'm pretty sure your problem is powdery mildew.

Re: resistance

1) Tomatoes are bred for resistance to specific diseases. If you get a variety that's resistant to late blight, spotted wilt virus, or fusarium wilt, it guarantees no advantage at all if your problem is powdery mildew. So it's important to know what problems you can regularly predict are likely to be problems for you and select varieties accordingly, if the primary strategy you want to use is growing resistant plant cultivars.

2) Resistance does not mean "immunity". Sometimes, resistance is very high, and you can more or less count on the variety to deal with the disease and not do anything extra. But most of the time, "resistance" really just means the plant fends off the disease longer and succumbs to it more slowly; you'll still have the disease and still have to deal with it.

Re: fungicide

Tomatoes are extremely susceptible to a wide variety of foliar diseases. Most people who successfully grow tomatoes start a fungicide regimen from the time they plant out, spraying regularly every week or two to prevent disease. This is because systemic diseases in plants can't be cured once they happen, and even most more or less surface diseases like powdery mildew are almost impossible to eradicate completely once you have them in on your plants. In addition, most remedies available to home gardeners aren't curative anyway. With disease, the important thing is to prevent, delay, and slow down disease. So you spray trying to prevent disease. Most of the time, you only manage to delay onset of disease--but this is helpful because it can mean the difference between plants that poop out early and those that can stay alive to give you a good harvest into late in the season. And slowing down disease progression is also important for the same reason.

Some ultra-organic gardeners do not spray any fungicides. But they employ a wide variety of strategies that are just as much work if not more work (foliar nutritional sprays, compost tea sprays, tons of work on the soil, constant monitoring and pruning of diseased foliage at the first sign, etc.). Others will use fungicides but stick to organic/biological ones. But in the vast majority of places tomatoes are grown, you have to do some form of active and regular disease prevention. Maybe you'll get some good seasons here and there when disease organisms are less present and conditions aren't conducive to disease. But counting on that could mean a lot of lost plants and harvests.