We have a women focused group in my company, which focuses on wellness, service and career growth, but everyone is invited.

Great topic. I do believe that there is value in having these types of events, but you are correct it does exclude those who do not identify as women. Perhaps discuss with HR what can be done to ensure that people who don't identify as one group or another has opportunities available so that they too can feel as if they belong.

Lots of great points above. The question I have is who/what group/why is the event being hosted? For example, I am very active in my local Women's Network. Because it is a Women's Network, our primary audience is women, however, we welcome anyone to join our events but there may be some that are more geared towards women. For example, we are hosting an event about how to prepare for being on camera and being on camera for virtual meetings, which contains great tips for all people. However, we've also had groups meet to connect on things like being a breastfeeding mother - sharing tips and tricks for pumping at work or while traveling, etc. Before specifically including or excluding, think about why, what's the goal, and what's the impact of the exclusion/inclusion. If you are trying to get one function or role together and you all happen to be women, sure, but think about it before moving forward.

Sometimes it can seem that only certain groups may be interested in a specific activity like 'virtual coffee'..... whenever possible try to be inclusive of all groups and let the uninterested groups have the option of saying 'no'. If it is possible to have an 'open' event to all for morale boosting that is usually more inclusive. Male, female, non-binary....not everyone in those groups is disinterested in certain activities or interested in them. If there is a particular group that has verbalized interest in getting together outside of work and wants to meet outside of work to connect, just start with those individuals since they have already expressed interest. Maybe in the future put it out to 'everyone'.

This is not a training or work related event. It is purely intended to be a fun event like a virtual coffee since most of us have not met each other for almost a year.

In general, I would probably avoid doing this because if it's women only, it excludes men and makes non-binary people wonder whether they would be welcome. If there is a very good reason to have separate groups for a training ,such as if there has been an incident in which several women were sexually harassed by someone who is now fired, having a separate workshop for women and men would make sense, with the understanding that anyone who is trans or non-binary may attend the workshop that is more comfortable for them. I think that doing this without a really important reason might have the opposite of the intended effect on morale; if it truly would be of benefit, proceed but with caution.

It's fine. This is the same logic that men use to justify why women should not have their own groups. Or white folks as to why any other race or nationality shouldn't have their own exclusive groups. It creates a space for a group of people who don't always have it. Nonbinary folks should absolutely have a place, as well, whether that's as part of the LGBTQIA+ groups or their own - that would be up to the environment of the workplace that has the diversity events.