From anecdotal reports it appears to me, that it varies between the different SSRI's how much they decrease the effects of psychedelics. It probably between people too, since we are all built differently. From all the reports found through google, there's clearly some kind of interaction going on.
Obviously, people are alway getting SSRI's prescribed for a reason - that signifies that you're not really in a good place, and when you're not in a good place, it's a big risk taking psychedelics. Not that psychedelics couldn't help - of cause they can - but you're making it a lot more risky.
LSD definitely helped me. On that first trip I experienced the deepest level of contentment that I had felt in years and it helped me identify that a lot of my anxiety is unnecessary. I was on Prozac at the time, I knew that SSRIs soften the trip, so with the assurance of having much more experienced friends around, I split a 10 strip with a friend. This is not HR advice, just my story.