A few years back somebody told me that he was "Submissive to Women".

What do you mean by "Submissive to Women" and how many connotations does it have?
What do you also mean by "Broad Minded People" and how many connotations does it have too?
Ok, I'll take this one then.

Both of these phrases can have fairly innocent meanings but I would guess, by the appearance of them both, that you were having a conversation about sexual preferences?

Someone who wants to be sexually submissive wants to be with someone who is sexually dominant and I suppose this can range from a bit of 'being in charge/confident' to the full-on dungeon scenarios. Actually, it's hard to think of a non-sexual meaning for this phrase. A man who wants to be submissive to women as a whole, rather than someone who perhaps is happy for his wife to 'wear the trousers', is probably thinking of sex.

Again, broad minded people can mean something in a more general sense, but perhaps that is better replaced by 'open-minded'. I think in this context he meant people who would try pretty much anything sexually.
Hello Guest

'Submissive to women': this could be used seriously, in a discussion of
a person's character, but more often it would be a jocular remark.

It means: 'I am usually ready to comply with the requests of
women'; or 'I am usually willing to do what women want me to do'.

The phrase often has sexual connotations, depending on context. Between
two males, after much alcohol, it is likely to be quite suggestive. Between
a patient and his psychotherapist, it could well be purely descriptive.

'Broadminded' means 'tolerant of other people's opinions or behaviour', or
'having liberal opinions'.

PS Sorry to crowd your thread, Guest - I didn't see it had already been answered.
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The connotations are not out of range of normal inference, Guest:

'Submissive' means 'willing to be dominated by', and 'broad-minded' means 'accepting of a wide range of moralities'.
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