I know quite a few men this age who rent, after divorce, selling house, etc. Prefering to be near their kids, not wanting to put down roots until next step, etc.
I also rent at 51 and the deciding factor in my 30's was due to not having children. I have lived all over the UK in some lovely places over the years, as was able to WFH.
I can think of many home owning men who I wouldn't touch with a bargepole!
Some very odd and outdated views on MN recently, or perhaps I never noticed it before 
I might be put off by a man who had few social interests or connections, with little interest outside of himself. I might be put off by a man with excessive personal baggage. But his status as the owner of a pile of bricks doesn't really come into it.
My close friend recently stalled on a 6 month old relationship with a fairly affluent homeowner with a property portfolio because he was drinking himself into oblivion behind closed doors.
Unless you want stakes in their home or to capitalise on their assets, why should it matter to you?