"Infective" or "Infectious"

You are right in saying that the word infective does not fit in the sentence "His enthusiasm was infectious."

NOAD says: "[...] infectious usually refers to the spread of positive things, such as good humor or optimism."

In this light, we should use the 'rule' exemplified by NOAD, as you said. So, in figurative sense we should say "His enthusiasm was infectious", not "His enthusiasm was infective." (See the NGRAM below.)

In order to answer your second question, first of all we should note that it is not true that "when talking about diseases, both the words seem to fit." In fact, as we can read in Merriam-Webster's Medical Dictionary, "infectious disease" is defined:

a disease caused by the entrance into the body of organisms which grow and multiply there;

while infective is defined:

producing or capable of producing infection.

In this light, it seems that infectious is referred to the process, while infective is referred to the agent.

However, for instance, we can usually speak of "infectious hepatitis", but not of "infective hepatitis" as OAD defines this usage "SPECIAL USAGE - DATED".

The following NGRAM describes 'enthusiasm was infectious', 'enthusiasm was infective', 'enthusiasm was contagious'.

Also, "enthusiasm was infectious" ("enthusiasm was contagious") gets 38,900 (50,200) hits on Google Books, while "enthusiasm was infective" gets 5 hits.

In the Ngram I also reported "enthusiasm was contagious" because in non-technical texts there is little or no distinction between infectious and contagious.

Infectious is one of the meanings of infective, but in my experience infectious is the more common word.

The NOAD reports that infectious means:

• [of a disease, or disease-causing organism] likely to be transmitted to people, organisms, etc., through the environment.
• likely to spread infection: "The dogs may still be infectious."
• likely to spread or influence others in a rapid manner: "Her enthusiasm is infectious."

Infective means:

• capable of causing infection.
• [dated] infectious: infective hepatitis.

When speaking, e.g., of enthusiasm you should use infectious.
Infective could be used as synonym of infectious, but the NOAD reports that usage is dated. There is a difference between the first meaning given for infectious, and the first meaning given for infective.

We can find in medical textbook and journals: "infective endocarditis" and "infectious endocarditis", as well, when talking about disease (mechanisms, process, cause, etiology). However, "infective" is more usual.

Examples:
• “Infective endocarditis” In: Goldman-Cecil Medicine, 2020 by Elsevier, 26th edition, section 8: Cardiovascular Disease, chapter 67
• “Infectious endocarditis” In: Textbook of Critical Care, 2017 by Elsevier, 7th edition, part 5: Cardiovascular, chapter 86
• “Infectious endocarditis” In: Textbook of Critical Care, 2017 by Elsevier, 7th edition, part 8: Infectious Diseases, chapter 128
• “Infective endocarditis” In: The New England Journal of Medicine [Clinical Practice], 2013, volume 368, pages 1425-1433