Drapes would muffle more sound than a wooden door hanging on a rail

Put up a curtain rod over the door mounted on a wall, and put a very thick quilt on it. It helps with cold on a house in a cold climate, so it should help with sound too.

Along those same lines you could by an inexpensive duvet cover and fill it with batting or insulation and hang it from a curtain rod with clip ons. It would be thicker and provide more of a barrier. You might be able to use 2 twins and hang them on swing away rods to get them out of the way when needed.

You're in a rental so you need soft furnishings--I'd mount quilts or some such thick decorative blankets that act as acoustical panels on any empty wall. Use RUGS if you don't have any. At work, some of the offices use a noise abatement machine (akin to a sound machine) to allow conversations with patients in rooms with hollow doors. They work extremely well. A sound machine would also do the trick.

A wooden door is another hard surface to REFLECT not DEFLECT the noise. You need something that will absorb the sound and that would be soft furnishings or specifically designed acoustical panels.

You can use a magnetic rod to hang thick fabric from the door (if the door is magnetic). I would try a sound machine before hanging anything on the door.

I cannot edit my post above about swing away rods to add these pics of what I mean:

if you choose thick curtains, I think it will be the most effective if they're hung in a way that they are pressed against the door (Like by using the swing rod Olychick posted above) and be sure they kind of seal all around it, especially the floor.

In addition to that: I found that changing my position can help. Sometimes when I can hear a noisy hotel neighbor behind the bed wall, I flip so my head is at the foot of the bed. Or sometimes merely changing the angle your ears are pointed helps too. These sound so minimal, but it actually makes a difference!

So in your apartment, try moving your favorite couch or chair to a different wall or corner. If you watch TV or listen to music, place the speakers at the noisy wall to help override other sounds coming from that direction. (this will also be nice for your neighbors, since it's a hallway wall instead of a shared living room wall.)

also, there are sound dampening curtains. these ones look nice, are not stupid expensive, and get good reviews. other brands are quite industrial looking, so you'd want to layer something decorative in front of them.

I also think if you use draperies that you should used heavy fabric, lined, and with many many pleats/folds.

I've dealt with sound issues before, and I'm sorry to say that there is no solution in a rental that will mask the bulk of the noise. Sorry, but it's sometimes easier to move than be continually annoyed by things you can't control.

one more thing to try: white noise. like, if you're watching a movie, and there's a really quiet scene that's disrupted by your neighbors, white noise will help mask that. you will need to turn up the general volume of your TV to balance it out (which may or may not disturb your neighbors, so keep that in mind). it will also be very helpful with sleeping. (I once lived in a place where I actually had to combine white noise with earplugs, it was that bad -- but it worked!)

if you have an iPhone or iPad, you can try out white noise right now! https://support.apple.com/guide/ipad/background-sounds-ipad5117c441/ipados

or if the sounds are really bad during the day, turn up the white noise and put on cordless headphones (noise cancelling would be best, but any kind is better than nothing). personally I'd hate to feel like I have to do that all the time at home, but if moving is not an option, this is effective.

Yes heavy curtains are the cheapest yet effective option for you.

@olychick Thank you! I like this idea.

@kudzu9 Unfortunately its not as easy to move, we just bought the place for one and renovated it and its not a rental. This is why I'm trying to do some creative thinking on how to resolve this sound issue since no one wants your conversations to be heard down the hall.... although it seems like no one else minds hahaha

@User I might actually try that white noise trick! I am also going to line the door with foam for it seals off the gap better and hopefully help to prevent sounds and smells from seeping in!

I wouldn't use drapes over the door, but if you have blank walls, mounting thick tapestries/quilts, etc, helps a great deal.

Amazon.com: HORV Door Curtain Thermal Insulated Doorway Curtain Noise Reduction Windproof Waterproof Door Cover Noise Barrier Soundproof Blanket Heavy Duty Cold Protection Door Screen 39 Sizes Optional : Tools & Home Improvement

This might work! (link above)

And, the link below is probably my favorite option but also the priciest:

https://www.google.com/shopping/product/1?q=sound+proof+door+curtain+roll+up&prds=epd:4036714325472665628,eto:4036714325472665628_0,pid:4036714325472665628&sa=X&ved=0ahUKEwjw4tbKjYP0AhVbl2oFHWe3DncQ9pwGCAU

Any air gaps will allow the transmission of air. You need to seal it completely, and make sure the door itself isn't transferring the sound waves. The tiniest gap will let in a surprising amount of sound. (Not a pro, but my boyfriend is...)