Could files downloaded from Youtube and Tumblr harm Mac? I'm putting old files to fresh Mac and on one external drive, there is bunch of video files I downloaded from Youtube and Tumblr at one point few months ago.

Would it be safe to put them to fresh Mac or could those files be harmful? There didn't seem to be anything bad with them before, but as this is fresh Mac I'm more careful now.

Should I keep them away from fresh Mac just in case?
Well there are two points to this. 

A.) there is a question of whether or not the files themselves contain any malicious code, which is hypothetically possible, but not likely. Owlswipe's comment is not correct in saying you cannot download files from YouTube, you can do so both through YouTube Red, as well as downloader extensions (which by the way are not illegal). 

All a YouTube downloader extension does is use a program (often times wget, or something similar) to make a copy of the video file that is referenced in the html for that video's page. While it is possible for a downloader extension to infect that video file, it is quite unlikely for it to happen in practice. As far as files from Tumblr go you can probably safely assume the majority of posters on Tumblr do not have the knowledge how, or a reason to inject malware into a picture they are posting. Also seeing as both of these sites use HTTPS (Secure HyperText Transfer Protocol) it would not be possible for someone else to slip malware into either the file as you were downloading it or the page when you were connecting. Though there is always technically the possibility that their severs could be hijacked, it is very unlikely that it happened during the specific time you were downloading files. Which brings me to the second point.

B.) Macs run macOS, which is built on Unix. Unix is very secure, and generally hard to infect with malware. While this does not mean you should stop caring about keeping your computer safe (because it is still possible for a Mac to get infected), as long as you don't enter your password into random prompts saying a program you didn't launch wants to modify your system you should be fine. Typically it is only Windows that is vulnerable to the type of attacks used by malware that is contained in an image or video file, and it is because of the way Windows handles both security access and multimedia with a connected system.

All in all your Mac should be fine if you move your older files to it. Unless you know for sure that someone had hijacked the YouTube or Tumblr servers on the day you downloaded the files, you don't realistically need to worry about it getting infected by them. With that said always be careful when running programs you download from the internet, even on a Mac, as it is easier for malware in a program to infect any system than it is for malware in a video or image file.