Render Blocking from Pagespeed Insights

Is there any way to work around this “suggestion” from Pagespeed to address render blocking issues?
Minifying all JS and CSS seems to break the site badly but this is the other thing that could be addressed.
Our mission is to rank higher as per the new Mobile test option in PageSpeed and in future this will impact on search rankings I believe.

I suppose it has to do with how the PP framework is built so not a quick solution?

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From: https://www.feedthebot.com/pagespeed/defer-loading-javascript.html
Why does it matter?
Google actively promotes and recommends prioritizing above the fold content so getting any resources at all (js, css, images, etc.) out of the critical rendering path is well worth the effort. If it makes your users happy, and it makes Google happy, you should probably do it.

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Eliminate render-blocking JavaScript and CSS in above-the-fold content
Your page has 5 blocking script resources and 11 blocking CSS resources. This causes a delay in rendering your page.

None of the above-the-fold content on your page could be rendered without waiting for the following resources to load. Try to defer or asynchronously load blocking resources, or inline the critical portions of those resources directly in the HTML.
Remove render-blocking JavaScript:

…ify/000000/aa108/index.include.296c3d.js
…-includes/js/jquery/jquery.js?ver=1.10.2
/…s/jquery/jquery-migrate.min.js?ver=1.2.1
…k/js/bootstrap-datetimepicker.js?ver=3.8

Optimize CSS Delivery of the following:

…/000000/aa108/default.include.4d6b59.css
…es/DT/framework/css/css.core.css?ver=3.8
…hemes/DT/framework/css/css.bootstrap.css
…mes/DT/framework/css/css.core_styles.css
…emes/DT/framework/css/css.datepicker.css
…s/css.core_childtheme_styles.css?ver=3.8
…css/css.bootstrap-responsive.css?ver=3.8
…template_basic_Practis/style.css?ver=3.8
…directory/wp-content/themes/DT/style.css
https://fonts.googleapis.com/css?family=Oswald