From the existing answers and what I've seen online elsewhere, there seem to be two main movements pushing for safe spaces with their own understanding of it.
a) A space where you should be open to speak your mind in a "civilized" manner.
In particular a space where you are heard out and your personal feelings and experiences not outright dismissed as false. And a space where your opinion is not dismissed explicitly or implicitly just because of who you are/to what group of people you can be attributed to (nationality, skin colour, sex, hair colour, clothing style, gender (identity) etc.). This includes no ad-hominem attacks. Note that this doesn't in its core deny factual discussion, the questioning of facts and depending on context even the questioning of experiences (in a respectful manner) if that is to further the meeting and not just to attack a person/invalidate their view because one cannot emphasize. It may, however, also include to not bring up topics (likely) offensive to a person involved in the meeting or drop a topic that turns out to be hurtful or offensive to a person. And this is then where it gets interesting and a safe space might lean in favour of minority groups (rather avoid topics potentially (perceived as) offensive to them) as a safeguard to skew the balance in their direction as to counter the fact that they might have less power otherwise. Here the free speech part gets a bit more interesting. But 1) for most organizational meetings there shouldn't be much (not necessarily no) risk to steer into that territory and 2) this is a general issue as without the safe-space it's the minorities who might be just shut down by the majority pressure. All in all the core goal is to provide a good open space to discuss, very much in line with an individualistic world view (judge people and their arguments based on their merits not their unrelated attributes). Note that I'm describing the general pattern/core concept, different people might grasp it slightly differently and implement it differently. A bit more on that below.
b) A space to let it all out
Another understanding for safe spaces seems to go more into a therapeutic direction: Allowing everyone to express their feelings, thoughts and experiences - typically centered around a particular topic. This applies to groups of women who want to discuss sexual harassments or trans-people or ethnic minorities etc. It's a space for them to discuss their impression of whatever *isms they experience in their daily life without being shut down because the majority cannot share these experiences, considers them invalid, or questions them as soon as they are brought up. It's not necessarily about finding an objective independent truth but about having a place where to express the respective feelings and potentially find allies. Here, often members of other groups or the group that is considered the main perpetrator are not allowed to speak up (or only in limited way) or even be present.
Variant a) makes (in its ... let's say ideal form) so much sense, it feels to me simply like another term for being a professional decent human. In my opinion all public and work life should follow that concept. Yes there will always be conflict around the fringes or say uncertainty where exactly being "decent" stops, what topics to bring up how in the given social norms or not at all and how to be honest while still being decent. The one spin I could see being special about safe spaces is to take extra care not to ignore and suppress minority voices. However, declaring something a safe space to me is the lazy route in that regard. It would be much more helpful to provide training in mechanisms that encourage minority group members or generally more quiet team members to speak up, e.g. like having the boss/loud group out of the meeting or required to stay quiet for x minutes etc.
If someone introduces this variant in an organization as a general concept, the goal and effect is probably to 1) encourage people who feel in the minority/shy to speak up in meetings and 2) to give people who feel being attacked/suppressed an argument to bring that up, e.g. with HR. It can communicate the message that the company wants a respectful environment. Why one would limit that to meetings only is beyond me^^ Obviously the concrete implementation and understanding can vary a bit - but in general this should not hinder free speech in meetings. It might shift the odds slightly in favour of otherwise overheard groups.
However, as all policies, ideologies etc it can be misused and perverted in its implementation. If you have a men-hater person in HR, they can get easier fodder now to pursue their victims and construe something (while it might be harder for a women-hater in HR to ignore complaints from women). Also notice that most people are somehow part of a minority, perhaps not one of the big ones, but even pineapple-pizza eaters should be encouraged in a safe space to bring up the idea to have that pizza type stocked in the company's fridge (for example) without being afraid to being ridiculed and shut down.
Now b) also makes sense, but only in dedicated settings. If applied everywhere in an organisation it would likely make that organization blind to factual truth. It could be powerful for political movements to re-enforce the conviction of their members but as it tries to protect one side from being suppressed by the other, it totally shuts out the other and thus isn't a good way to find a balanced solution that works for everyone. So applying this approach to company meetings seems weird.
In general, there seem to be a few main problems when introducing a "safe space" approach that I see a pattern of (second hand only so far):
- both concepts often get mixed. Safe spaces that are ridiculed and feared by some in universities seem to lean strongly into the b) group (or at least their perception) but applied to a broad range of meetings or even general everyday interactions such that it conflicts with the general purpose of a university (open debate and critical thinking and interaction).
- Implementations suck. As most good ideas, the implementations often fall way behind of what the authors of the good ideas wanted to achieve. Especially regarding such social struggles where emotions and group behaviour often get in the way of good implementations.
- Good ideas and concepts can be perverted. Ideologies that are good in essence tend to attract support from people. But that also makes them a good tool to mislead people (consciously or subconsciously). You claim to follow a universally good goal, everyone hops on board and starts rowing, but the steering is totally off and everyone ends up being the voluntary slave rowers of a war galleon going in the wrong direction and sinking their own fleet. An overzealous minority group supporter might for instance just push their own group and agendas with the concept and suppress everyone else having the backing of the public for pursuing the good cause. Or even perverting the concept in prohibiting addressing crucial issues like sexual assault because it might trigger someone else.
- A good portion of the critique of safe spaces is probably also perception - as even with a good implementation of the a) concept some balance re-adjustment can be made and if it works more minority opinions can be heard. People often don't like their views being challenged and having suppressed minorities speak openly can be a major challenge to a majority complacent in their status quo. And equally a majority member voicing their opinion can easily be misread as an attack if it doesn't comply
with a minority position especially in the heated climate some part
of the West is currently in regarding some topics.
All in all, no one can tell you in advance whether your implementation of a safe space will be limiting to free speech for you or liberating. It depends on the actual understanding by your superiors of the concept and how
well thought out the implementation is. You can maybe gauge by the language used whether it falls more into category a) or b). The more towards b) it goes the more you might feel worried (if it is applied broadly and you care about 'truth finding' in your meetings).
Otherwise my advice would be to consider it a reminder to be decent enough to really hear others and respect their point of view. And take it as encouragement to speak up - in respectful ways. Rather questioning and providing your perspective when criticising something that is subjective in nature than assuming your opinion is shared universally. Just because you like Salami pizza, not everyone needs to, is a good thing to keep in mind, in general.