I posted this here already but it is still relevant the original question.
I have had similar issues with space between columns. The root problem is that columns in bootstrap 3 and 4 use padding instead of margin. So background colors for two adjacent columns touch each other.
I found a solution that fit our problem and will most likely work for most people trying to space columns and maintain the same gutter widths as the rest of the grid system.
This was the end result we were going for

Having the gap with a drop shadow between columns was problematic. We did not want extra space between columns. We just wanted the gutters to be "transparent" so the background color of the site would appear between two white columns.
this is the markup for the two columns
<div class="row">
<div class="col-sm-7">
<div class="raised-block">
<h3>Facebook</h3>
</div>
</div>
<div class="col-sm-5">
<div class="raised-block">
<h3>Tweets</h3>
</div>
</div>
</div>
CSS
.raised-block {
background-color: #fff;
margin-bottom: 10px;
margin-left: 0;
margin-right: -0.625rem; // for us 0.625rem == 10px
padding-left: 0.625rem;
padding-right: 0.625rem;
}
@media (max-width: 33.9em){ // this is for our mobile layout where columns stack
.raised-block {
margin-left: -0.625rem;
}
}
.row [class^="col-"]:first-child>.raised-block {
// this is so the first column has no margin so it will not be "indented"
margin-left: -0.625rem;
}
This approach does require an inner div with negative margins just like the "row" class bootstrap uses. And this div, we called it "raised-block", must be the direct sibling of a column
This way you still get proper padding inside your columns. I have seen solutions that appear to work by creating space, but unfortunately the columns they create have extra padding on either side of the row so it ends up making the row thinner that the grid layout was designed for. If you look at the image for the desired look, this would mean the two columns together would be smaller than the one larger one on top which breaks the natural structure of the grid.
The major drawback to this approach is that it requires extra markup wrapping the content of each columns. For us this works because only specific columns needed space between them to achieve the desired look.
Hope this helps