There are lots of pros and cons to this. In the end, you'll have to determine if it'll work for your shop.
Here are some things to consider:
Shipping is never free. Someone has to pay the post office or the company doing the shipping. However, you can always add in your shipping costs into the price of the item. (Make sure to set international shipping as extra, though. Free shipping doesn't necessarily have to be free international shipping.)
But, a shopper is more likely to choose an item that has "free" shipping, so you might find that you're making more sales this way.
Etsy is prioritizing items that have free shipping, highlighting those items and helping them with ranking. This may make your products more visible to shoppers. More shoppers seeing your items may translate to more sales.
However, more sales where you're losing money on the endeavor will only hurt you in the long run. You still need to be making a profit.
Consider volume. If you're selling more, a smaller profit per item won't make that much of a difference. But this only works if you can reasonably make a lot of that item. You can only sell what product you have on hand (or can make in the time allotted.)
Etsy made a video to encourage sellers to offer free shipping (their article about the same is here):
If you're not sure if you can do this, take a look at other sellers who have comparable items. What are they charging? Do they have free shipping?
Keep in mind, you don't need to have the cheapest price to remain competitive. Some buyers won't buy the cheapest of the choices due to a perception that it is lower quality. And if your shipping is free...
You might be surprised how much wiggle room you have in this. Just something to consider. In the end, do what is right for your shop. Don't be pressured into offering free shipping if you absolutely cannot do it.
Do you offer free shipping? Did you find it easier or harder to implement than you thought?