I believe the sentence from the RFC:

[XHTML1] defines a profile of use of XHTML which is compatible with HTML 4.01

is technically incorrect. While the XHTML 1 compatibility profile was compatible with HTML 4 as implemented by major browsers, that wasn't actually HTML 4. HTML 4 is based on SGML, while what was implemented was a combination of HTML 4 semantics with the tagsoup parsing rules that browsers organically developed. These rules were only later formalized as part of HTML 5.

The compatibility guidelines do recommend a space between <br and />, but (at least according to https://validator.w3.org/ in HTML 4 mode) this doesn't change anything about <br /> being a NET-enabling start-tag <br /, followed by a greather-than sign.

Enter this:

  <h1>Hello<br />world</h1>

and select "Validate HTML fragment", "HTML 4.01", and "Show Outline". This is the result:

  [H1] Hello>world

(Obviously nitpicking, but that's my point: the nitpickers can be out-nitpicked.)