Is it possible to change the titles on the Meta tag widget?

If you are referring to the default meta tag widget that shows when you have no widgets in an activated sidebar the answer is you would have to go into the code somewhere. If you add the widget to the sidebar then all you have to do is type a new title in.

I mean the one with the RSS feeds and logon, register links and stuff. I just want them to say something more to my taste

Those are the default widgets which just serve as a place holder. Just go to Appearance>Widgets and add the widgets you want to the sidebar and you can rename the title.

You'll have to explain a little better. What are the widgets you have in your sidebars (go to dashboard->appearances->widgets) and which one do you want to change?

The widget is the "Meta".

What I really want to do is just change the narrative on "RSS feeds" and Admin

The 'Meta' widget is part of wordpress and you will have to edit the wordpress code to change it.
You could do a google search using 'wordpress meta widget' and see what you find

I could just put a text widget in, but it would lose the Log In/LogOut logic which would then look messy.

You would think there would be a table somewhere that could be modified.

There are all sorts of plugins for login/logout, meta, rss, etc. Just design your own "meta" widget by using several.

HINT: do a google search using 'wordpress meta widget' and see what you find