In English it's more natural to say "Do you have brothers or sisters?" Is "Máš bratry nebo sestry?" unnatural or incorrect in Czech?
None of them is too common in Czech. We normally ask "Máš (nějaké(ho)) sourozence?" (either plural or singular).
Other options are less common. Máš bratra nebo sestru? bráchu nebo ségru?
The corpus clearly shows we use the singular much more often than the plural.
A direct comparison: "bratra nebo sestru" 86 hits, "sestru nebo bratra" 21 hits. Regardless of context, often with some different verb.
"nějaké sourozence" 92 hits, often in connection with "máte" or "máš", "nějakého sourozence" 19 hits.