Problem
<!DOCTYPE html>
<html>
  <head>
    <title>SVG Filter</title>
  </head>
  <body>
    <h1>SVG Filter</h1>

    <svg xmlns="http://www.w3.org/2000/svg">
      <defs>
        <filter id="filter">
          <feGaussianBlur in="SourceGraphic" stdDeviation="5" />
        </filter>
      </defs>
      <image
        id="myImage1"
        href="image.jpg"
        x="10"
        y="10"
        height="100px"
        width="100px"
        filter="url(#filter)"
      />
    </svg>

    <svg xmlns="http://www.w3.org/2000/svg">
      <defs>
        <filter id="filter">
          <feColorMatrix
            in="SourceGraphic"
            type="matrix"
            values="1 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 1 0"
          />
        </filter>
      </defs>
      <image
        id="myImage2"
        href="image.jpg"
        x="10"
        y="10"
        height="100px"
        width="100px"
        filter="url(#filter)"
      />
    </svg>
  </body>
</html>
Solution

The filter on the SVG has a duplicate id of filter causing the second svg to apply the filter from the first. To fix this, ensure that each relevant element has a unique id.

<!DOCTYPE html>
<html>
  <head>
    <title>SVG Filter</title>
  </head>
  <body>
    <h1>SVG Filter</h1>

    <svg xmlns="http://www.w3.org/2000/svg">
      <defs>
        <filter id="filter">
          <feGaussianBlur in="SourceGraphic" stdDeviation="5" />
        </filter>
      </defs>
      <image
        id="myImage1"
        href="image.jpg"
        x="10"
        y="10"
        height="100px"
        width="100px"
        filter="url(#filter)"
      />
    </svg>

    <svg xmlns="http://www.w3.org/2000/svg">
      <defs>
        <filter id="filter2">
          <feColorMatrix
            in="SourceGraphic"
            type="matrix"
            values="1 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 1 0"
          />
        </filter>
      </defs>
      <image
        id="myImage2"
        href="image.jpg"
        x="10"
        y="10"
        height="100px"
        width="100px"
        filter="url(#filter2)"
      />
    </svg>
  </body>
</html>