This resonates with me.
I became a SAHD (though with some part time work chucked in) not long before the pandemic when we moved to my DP's home city to be closer to family. I thought it would a doddle socially. Up in London there were a fair few SAHDs and I didn't think I'd be blazing any trails.
I was delighted when my DD came back from her new primary school on the second day with a note from the class PTA representative welcoming us to the school, telling of all the social activities there are and with an invitation to join a Whatsapp group 'for lost jumpers, help with pickups, coffee meetups etc'.
Looking forward to making some contacts in a new city, I sent an email back giving me and my DP's numbers, explaining that I was a SAHD and volunteering my services for PTA fundraising events.
A few weeks pass and I don't hear anything, which seemed a bit strange, and one night my DP says she'd been added to the WhatsApp group. Eventually the class representative comes up to me at the school gates and says she can't add me to the Whatsapp group because 'it's for mums' and since they meet for coffee sometimes 'you wouldn't be interested in that sort of thing'. She helpfully adds that I can always start my own class dads' Whatsapp group. I try to explain that since I'm new to the city I don't know any of the dads but at this point she's already moving away to talk to someone else.
After a term of my DP forwarding to me useful messages from the group whilst at work, she felt she was in with them enough to appeal over the head of the class representative to the other mums, who agreed to let me to join. But this encounter has sadly set the tone for my attempts to fend off social isolation as a SAHD and, if not actually make friends, form some sort of peer group.
Social events connected with the class are invariably labelled mums' nights or mums' meet ups. Invitations to parties and playdates for our DCs usually get sent to my DP. It's doesn't seem to make any difference how many times I'm seen at the school gates or in the park with the kids. There was just one occasion where a party invite for my DS was sent just to me and I was almost overcome, I was like 'oh thank you thank you, someone recognises what I do!'
I tired to break the mould when my DS started reception. I started a class PARENTS Whatsapp group, got mums and dads to join, and a few meetups were organised off the back of that. Chat got completely dominated by a group of 6-8 mums though and I watched in horror as the dads dropped out of the group one by one. Things eventually fell into a familiar pattern.
I'm still plugging away at it. I love spending the time with the kids and this is what's best for my family. I just wish it wasn't seen as such as oddball thing for a man to do and the potential psychological impact bothers me.
I know a few chaps who would be well suited to being a SAHD and from a social perspective I'd love to see more dads at the school gates as a counterpoint to more women in boardrooms. But at this point I'd only really recommend it to dads would enjoy their own company (and that of small children).