I think you are overthinking this. If a business contact mentions her company is bidding on a certain govnerment contract, and the typical winners of that contract are companies which are much larger and more sophisticated than hers, saying the contract is out of your league is hardly going to be interpreted as a romantic reference. If you're talking about a perceived mismatch in a platonic friendship, I think the deeper question would be about what you value in a friendship.

@choster I'm referring to someone declining to express an opinion in a discussion, or outright leaving a discussion, because someone else in it is out of the first person's league. In your example it wouldn't, indeed, seem like a problem.

One way of avoiding the romantic liaison is "He/she is not my type."

@ispiro Perhaps I don't understand how you would use the expression. This is why we require word and phrase requests to include a sample sentence for how it woul be used. There is no implication of a romantic interest simply for saying a certain discussion is out of your league.

@choster I didn't know of that requirement. Fixed now. Please feel free to edit it and edit its styling. In your example there would be no problem because of explicitly stating that it is the discussion that is out of my league.

@ispiro I understood the question to be asking for an alternative to “Out of my league” when avoiding a romantic situation. Whether "not my type" is true or not isn't relevant

@WeatherVane So I indeed misunderstood your comment. But I still don't understand it. Saying to someone "you're not my type" doesn't mean the same thing as "you're out of my league".

American sports are often organized by leagues—groups of teams that play against each other. In baseball there’s major league baseball and the minor leagues. A weak player gets “sent back to the minors.”. Out of my league is a metaphor for any challenge one is not capable of handling, be it romantic, financial, technical, professional, social.

@Xanne Yes. That is the source of the expression, and its general meaning. But if you search the web you'll see what I mean that it is used quite a bit to mean in a romantic fashion.

Then avoid it, if you’re concerned about misunderstanding. Only linguistically of interest if you demonstrate that other uses have declined.

The entire premise of the question is wrong. Out of my league most certainly does not refer only to something romantic. If that's the claim, then show some evidence of it.

@JasonBassford See edit.

Do not bury the main question in a lengthy post. Highlight it.

"I felt it I should be formal with my potential supervisor because we are not peers, so addressing him by his first name was a no-no;" "Adam Elga's idea is that if we disagree on a wide-ranging number of issues, then we have good reason to think we are not peers."

'You're out of my league' is a problem here for me not because of the potential-involvement-related connotation (yes, present, but surely negligible in the context given) but because it's over-effusive. @David's toned-down suggestions are far more appropriate.