I think a rule of thumb is minimal interactions with other drugs/substances, unless they potentiate the effects or they neutralize others. I've always read that with many drugs, the best policy is to ensure you're not taking them alongside significantly more drugs. It means generally that there's more added into the mix and so more variables for things to go both ways; good and bad. That's the best practice, in my opinion. Having said that, we're not dealing with something that has significantly more risks unlike other drugs. Looking up combinations with mushrooms the only really concerning combinations is tramadol. Potentially concerning ones are stimulants; coke, speed. And cannabis gets a good mention as well seeing as it can give psychedelics a massive kick, one that's perhaps not always welcome because it can get way more intense.
I got this information from here:
combo.tripsit.me
I always reduce whatever medication I'm on for psychedelic experiences. Common knowledge is that they reduce the effects and this makes sense because they work on similiar neurotransmitters that psychedelics work on, serotonin being a huge component in a psychedelic trip. Anti-depressants (at least this is how we believe they work) work by inhibiting the re-uptake of serotonin when it has done it's job helping messages jump across the synapses in our brain that is responsible for essentially the operating of our brain. It's believed serotonin plays a significant role in ensuring messages get from one nerve ending to another. We have receptor sites which serotonin is absorbed into and SSRI's prevent this absorption from happening so that theoretically there is more serotonin freely available. More serotonin, as per the medical model sees it, means more happiness, better sleep, memory, mood etc.
www.ocduk.org
(The above link is SSRI's used for OCD, but SSRIs are used in the same way across all sorts of mental health and related issues so information here regarding the medication still applies)
When you have psychedelics attempting to attach themselves to the same, or similiar, receptor sites, you potentially have a conflict. Current understanding of psychedelics is they do indeed attach themselves to particular serotonin receptor sites. So the result will likely be a reduced experience.
More info here:
Serotonergic psychedelics (also known as serotonergic hallucinogens) are a class of hallucinogenic substances with a method of action strongly tied to modifying the normal neurotransmission of serotonin in the central nervous system (CNS).
psychonautwiki.org
All that being said, it's a choice between your health and wellbeing, or having a trip. The likelihood of antidepressants affecting you in a serious way are slim, unless you take MAOI's in which case DO NOT EVER ATTEMPT THIS COMBINATION. Then again, by taking psychedelics and being on them, your trip probably won't be the same. It might be significantly reduced actually. I obviously would never expect someone to stop taking their meds purely for a psychedelic trip. It depends on what meds, why you take them, how much you need them, withdrawal effects, need for tapering and reducing therapeutic levels in the blood stream.
It's better not to be taking anything while you take whatever it is you are taking, in an ideal world. The only difference is, we don't live in an ideal world and so real life has to factor in which inevitably means understanding our situation and making informed decisions.