Can’t work out how I feel about this

It's not a flatshare. It's OP's home.

The thing is OP, many men wouldn't want to lodge with your family, they'd find tiptoeing around the children and the need for extra care about modesty / dignity a bit of a pain, or a potential concern. Finding a lodger is all about finding the right match. You identify what you do and don't want in a lodger, potential lodgers do likewise and you see who seems to match which host.

I live alone, and I've had several lodgers, male and female. I tend not to advertise, but instead search on a well known site and PM people who sound like a good fit. In my city, it's much easier to find male lodgers, who tend to want a Monday-to-Friday let. I've not had any bad experiences (well, one of the men was hoovering at inappropriately late hours because he didn't tell me he had a cat allergy: presence of cats was clear in my ad...), but still, if I search for another lodger in the future, I'll tend to message women before men. And since I'm inviting someone into my house, it's my choice!

Even a man living alone with two children, one a young teen would probably hesitate to have a (stranger) male lodger. Go figure.

Not to mention that the OP is neither a limited company nor a public funded body therefore does not have to comply with any legislation of any kind

Anti- discrimination law is not restricted to limited companies and public bodies.

The OP can advertise for a female only lodger. Advice from what seems a sensible letting site is to frame it along the lines of We prefer a female flatmate as all the other flatmates are female rather than "no men" or "only women"

Is the OP going to ban her lodger having male visitors or a male partner staying over?

She could advertise for a single white rich lodger if she so wished.

Not true as that would be racist and against the law.

You can of course advertise for a female.

Of course it’s legal to advertise for women only!

Sex is a protected characteristic under the Equality Act so any business could exclude people on the basis of providing a single sex provision if it was appropriate.

Not to mention that the OP is neither a limited company nor a public funded body therefore does not have to comply with any legislation of any kind.

She could advertise for a single white rich lodger if she so wished.

That's good then

Of course it's legal. Her home is not a business, it's her home.

Is it legal to advertise for female only?

I mean I have no idea but op should check before doing so probably.

There’s no need to discuss why you want a woman as a lodger let alone feel the need to justify it

It is absolutely fine to only let go a woman

Female tenant only is what I would say and when I’ve rented out it’s only been to women. You don’t have to justify anything. You are safer with a female tenant.

YANBU. I wouldn't dream of it.

You would feel safer with a woman because you would be safer.

Simple and true.

I'd add, I'm interested in your 'feeling bad', because if that's for yourself, as you might be missing out on a really nice lodger that happens to be male, that's one thing.

But, as you say, you wouldn't feel comfortable with a man in your home, so you wouldn't actually be missing out.

They're not stray cats though. Feeling sorry for them and wanting to adopt them isn't rational or relevant.

YANBU. Your first and only priority is the safety of you and your children.

Absolutely only rent to a woman.

So say 'women only' in your advert. Simple.

I'm surprised you even have to think about this.

You may get a few stroppy men contacting you - to prove their personal self-selecting undesirable status. Ignore them.

We really need to stop teaching women to ignore our boundaries in order to ‘be kind’. Just ask yourself who that benefits.

OP statistics tell us that you will be safer with a woman. Your own subconscious is telling you that you will be safer with a woman.

Does anyone know if there's an issue with advertising for "women only" in this case? I would have thought/hoped not as this person is living in their home, but I know it's not allowed in other contexts such as job descriptions, etc

Leaving aside the massive issue of safety, there is also comfort and dignity. I would feel I had to apply more rules to myself about proper appearance more like I'd apply if I were leaving the house (like no tops for slobbing round that are a bit too big and sometimes can show a bit of side boob, think twice about short pyjama shorts).

I also have a thing about cleaning up after men. So whatever extra work were created by having a male lodger would irritate me more than the same work caused by a female lodger. Probably wrong of me but it would spoil my day.

Again on sexual politics, having to tell a man to please tidy up if he's left the shared kitchen in a state, feels different to telling a woman. You get into the politics of expectations and nagging.

Tbh I could do without it and if I had a decent female applying I'd probably take her as a result.

I say to myself one day it could be my lovely sons having trouble finding a place so am I being awful? Then I think, no, there are plenty of men who need lodgers too and women who aren't as bothered as me. Also a woman I definitely had less choice than the men when I was looking for houseshares when young. So so many places where I was like fuck no, I am not sharing with those dickheads or having that landlord anywhere near me. Viewings were always done with a friend and we fairly often found ourselves doing the signal of that's a no, let's get out of here quickly and quietly no fuss

So on balance I say go ahead and take females only without feeling bad.

We used to pre Covid host international foreign students we have 2 girls ourselves and dh absolute rule is we host girls only. Their room next our dds on top floor. Not happening.

God I wouldn’t even consider having a man

It's your home and your right to decide who you share it with. You have children, therefore it's even more important to ensure safety and security. Women are statistically a much safer bet than men. It's still important to assess any potential lodger as carefully as possible, but nothing wrong in wanting only women to share your home with.