Well, when it comes to the issue of slavery, within a medieval setting, using all the tropes of the highly problematic 'great white liberator' story that has a long and very troubling history, yes it does involve race.
I would be fine with Dany rescuing the slaves if any effort was put to show that the slaves themselves were active agents in their own liberation, helping bring down Yunkai, which would have made its liberation more believable than sneaking a gate open. It is problematic because the series goes to painstaking lengths to show that while it is a noble-centred series, the people are still influential, and moreover, have active interests. The show, I cannot speak for the books but I imagine them as well, is highly concerned with lifting as much inspiration from real medieval societies as possible in how they operated.
This makes Dany's story troubling, because she is increasingly operating in a setting that has no real-world analogue or precedent, and seems incredibly fantastic, in the worst way. A slave society that isn't highly paranoid about revolts? Slaves that are entirely passive in a city with a would-be conqueror at its gates? It not only brings in a problematic racial element whereby the only time in the show that the common folk are entirely passive is when they are brown and slaves, with a pure white person needed to rescue them, but it is also problematic because it is so at odds with the rest of the show which lifts inspiration from real world societies. The end result is that it comes across as white man's burden played out in Conan the Barbarian while the rest of the narrative is above such shenanigans. That is why people are bringing race into it: because it features a great mass of childlike brown slaves who are saved by a destiny child white woman in a series that strives for a complex display of high-born/low-born interests and interactions.
And it came just after a whole sequence of talks about such things, only to reduce the masses at the end to a blubbering group calling for their 'mother,' which also has a lot of really racialised historical implications. THAT is why people are bringing race into it.