I use a custom script to open all post and external links on the front page in a new tab. Based on a script I found online but customised to beehaw specifically.

// ==UserScript==
// @name         beehaw - Open links in new tab
// @description  Open links in new tab. Ctrl-click or Middle-click loads it in background
// @match      http*://*beehaw.org/home*
// @match      http*://*beehaw.org
// @version      0.0.1
// @grant        GM_openInTab
// @run-at       document-start
// ==/UserScript==

var suppressing, clickedElement;

window.addEventListener('mousedown', function (e) {
  clickedElement = e.target;
}, true);

window.addEventListener('mouseup', function (e) {
  if (e.button > 1 || e.altKey || e.target != clickedElement) {
    return;
  }
  var link = e.target.closest('a');

  if (!link || !link.href) {
      return;
  }

  if (link.getAttributeNode('aria-label') && link.getAttributeNode('aria-label').value == 'Expand here') {
      return;
  }

  if (link.href.startsWith('https://beehaw.org') && !link.href.startsWith('https://beehaw.org/post/')) {
    return;
  }

  GM_openInTab(link.href, {
    active: !e.button && !e.ctrlKey,
    setParent: true,
    insert: true,
  });
  suppressing = true;
  setTimeout(function () {
    window.dispatchEvent(new MouseEvent('mouseup', {bubbles: true}));
  });
  prevent(e);
}, true);

window.addEventListener('click', prevent, true);
window.addEventListener('auxclick', prevent, true);

function prevent(e) {
  if (!suppressing) {
    return;
  }
  e.preventDefault();
  e.stopPropagation();
  e.stopImmediatePropagation();
  setTimeout(function () {
    suppressing = false;
  }, 100);
}

For Mastodon there’s FediAct or Mastodon - Simplified Federation.