As Joshua Engel notes, temperature is really the most salient point. Brewing tea at a lower temperature will change the flavor notes that emerge (because of different solubilities of different components at various temperatures). If adding milk lowers the brewing temperature, it will definitely change the flavor.
That's probably the source of the common belief that adding milk during steeping will decrease astringency of tea. In that case, it's likely that simply the lowering of the steeping temperature is actually causing the decrease in astringent tea compounds, which are less soluble at lower temperatures. (This decrease in astringency -- which is a common flavor feature of many teas -- is probably also the source of the belief among some that adding milk during steeping will decrease flavor overall.)
But that's not the only issue. As noted here:
the presence of other components in the brewing water, such as
minerals and proteins from milk, affect the rate of extraction, and
therefore the flavor.
However, that link goes on to note, "For most people this isn’t a concern, though, because they judge the strength of the brewed tea based on its color and pour in the milk after removing the bag." And if you're the sort of person who just dunks a tea bag in water until it's "the right color," when you add the milk isn't likely to be a major concern in flavor. If you're more careful about steeping, e.g., measuring the amount of tea precisely, measuring steep time, ensuring a consistent brew temperature, etc., then you might be more likely to notice a minor difference even if the milk is heated and added earlier.
And sometimes the difference in flavor can be quite noticeable, depending on the type of milk and the precise flavor compounds in the tea (which may be more or less soluble in milk). For example, see this informal experiment with ginger "tea." (I put "tea" in quotation marks because the "tea" in question contained no tea leaves. Some people consider "herbal infusions" to be "tea"; others don't use that term. The question is ambiguous, so I'm assuming a broad definition here.)
While it's hardly a rigorous experimental method, it seems that the blind taster here found that the ginger flavor was enhanced by adding milk during brewing. Moreover, the higher the fat content of the milk, the greater this effect (most likely due to fat-soluble compounds), with half-and-half producing an even more significant effect than plain milk.
Other spiced teas (including spiced black teas, rather than simply herbal infusions) also frequently make use of this effect. Chai tea is one of the more traditional examples, where the "one pot method" generally involves steeping at least part of the time with the added milk.
More generally, adding milk during brewing is therefore likely to affect the flavor balance in some way, but the particular impact will likely vary depending on the type of tea and its particular flavor components. As with most things, the best advice is probably just to try brewing it both ways for your favorite teas, and see which you like better.
I did a brief search for examples of more rigorous scientific studies on the issue of milk and tea component solubility, but I didn't find anything quickly. (I'm not saying there isn't anything out there, but nothing came up in top hits for a couple searches.) Instead, the most common debate about milk and tea seems to be about whether adding it impacts its health effects (see here for a recent review of the literature). Adding milk does change the tea chemistry in various ways, as noted there, but there doesn't seem to be much research on brewing in milk.
One final issue that may impact this question is denaturing of milk proteins, which can happen when they are overheated. This mostly comes up in the perennial debate about whether to add milk to the cup before or after tea. The Royal Society of Chemistry gave a ruling on this point long ago, claiming that putting milk in the cup first allowed a more even heating of the milk and thereby decreased possibilities of "clumping," "skin," and other marks of milk degradation when heated. I bring this last point up because obviously brewing the tea along with the milk will also have an impact on this issue. And if you're brewing tea with a bag in a mug (rather than a separate pot for brewing), adding the milk before brewing would be the only way to follow this advice. (In any event, the impact on the milk is probably not even noticeable to many; hence the debate on when to add the milk in general.)