My tentative hypothesis: the less difference there is, the more important it becomes to signal it.

Me too.

I noticed that at least here in Germany childrens toys are presented much more gender specifically than they used to - think pink ponys and armed space rangers. But also boys books and girls books. I think this is more than just improved marketing. The entire domains of boys toys and girls toys diverge. Previously often one set of toys was sold for and used by boys and girls alike. The play differentiated along roles but still overlapped. But ot any longer. I wondered: Why is that?

TLDR: When roles do no more work to match expectations of the other gender the need to do so is satisfied by choosing other aspects of interests and behavior that pattern-match against these expectations.

My reasoning was as follows:

Assume that there are optimum male and female stereotypes with respect to preferrability and that these are known to both genders. Stereotypes mean combinations of observable properties or behaviors that pattern-match against the optimum stereotype.

This is plausible: At least for body attractiveness preferences are closely modelled by the other gender according to this study so I'd guess that basically the same holds for other aspects of preferrability (and status in case status being gender-specfic).

Traditionally many properties did align with (gender-specific) roles - roles actually being kind of stereotypes - or more precise: The optimum stereotypes projected down to the properties captured by the roles. So matching a role automatically netted you a fair match on the optimum stereotype.

But if roles do no longer work as a vehicle for this pattern-match because the roles are stripped of their differentiation potential via societies changed perception of roles - by precisely taking gender out of the roles the remaining pattern-match is weak. But the need to learn and aquire a match of the optimum stereotype doesn't go away. The pressure just goes to other areas - interests, preferrences - that pattern-match against the stereotype (which presuably also slowly changes).

Side-note: In the toy-case whether this pattern-matching was done by children or by their parents doesn't matter much for this discussion.