Just some food for thought.
On Space.SE, all the
[manned-xxx] tags have been made synonyms of
[crewed-xxx] tags, e.g.
[manned-spaceflight] has become synonym with
[crewed-spaceflight], with the
[crewed-xxx] tags being the main tags and the other ones redirecting to them.
This follows a movement in the spaceflight community and industry to prefer the term "crewed". You can also see this in the media, the term "crewed spaceflight" has become more and more prevalent. You can see it in new titles like "SpaceX optimistic about May crewed mission [...]".
Yes, technically "manned" refers to all genders. For a long time I thought nothing of it and dismissed criticism of the term with the same arguments brought in some answers here (that it includes all genders, so there is no problem). But inclusive language starts small.
Wikipedia has also moved away from the term "manned spaceflight" and uses "human spaceflight" and "crewed spaceflight" or "crewed spacecraft" instead of "manned spacecraft".
NASA has changed their language in 2012, and now has this to say in their style guide:
Gender-Specific Language (e.g., Manned Space Program vs. Human Space Program)
In general, all references to the space program should be non-gender-specific (e.g., human, piloted, unpiloted, robotic, as opposed to manned or unmanned). The exception to the rule is when referring to the Manned Spaceflight Center (also known as the Manned Spacecraft Center), the predecessor of Johnson Space Center in Houston, or to any other historical program name or official title that included “manned” (e.g., Associate Administrator for Manned Spaceflight).
I realize Aviation.SE is not Space.SE. But there is a reason why it is called the aerospace industry, the fields have certainly a lot of overlap. And I realize that changing ones way to speak without seeing a problem oneself isn't something one wants to do. But on the other hand, using a more neutral term doesn't hurt, either.
The argument of Google showing more results for "manned" then for "crewed" is also not a good one. The term "manned" has been used for a long time, so historic documents will still use it, and it will obviously take a while to become completely obsolete.
So my plea would be that it doesn't hurt to be mindful of inclusive and gender-neutral language and phase out "manned" and "unmanned". For "manned", "crewed", "human" or "piloted" (if applicable) can be used, for "unmanned" good alternatives are "uncrewed", "robotic", "remote-controlled" or "autonomous", depending on context.