I'm making my first starter and I accidentally pitched the yeast when the wort was still warm. I've had it on the stir plate for 24 hours and then a 30 minute rest. See picture, is it still ok to use for beer?
Most ale yeast can survive some fairly warm temperatures. In some of the upper ranges, yeast will tend to produce more non-alcohol by-products than you probably want in a beer but it will still be alive and well. I would say that as long as both the starter and the beer you pitched it into are less than about 100°F and you brought the wort down to a more appropriate fermentation temperature fairly quickly, then you'll probably be just fine.
If there's a big differential between your starter and your somewhat cooled wart, you might negatively impact yeast health (and thus the quality of fermentation), but for "reasonable" differentials (10-15°F), I have never run into any problem.
My advice would be to quickly bring the wort to the recommended fermentation temperature and keep it there. At the tail end of fermentation, you might raise the temperature a few degrees so that the yeast has an extra opportunity to clean up any off flavors, but I certainly wouldn't stress out about it.
It looks like the yeast are still in suspension to some degree after the 30 min rest indicating they are still alive and you should be ok.
As an extra check, take a gravity reading once the yeast have fully settled. If it's close to your expected FG then that confirms the yeast were active. You could also taste the gravity sample. Starters often taste yeasty, or have lots of green beer flavour, but if it tastes meaty, rubbery or other off flavours then you know it's not good.