In almost every article about asthma there is some kind of mention that
you can do sports with asthma. There have been even Olympic medalists suffering from it.
Several links (all of them in Czech, sorry)
Is that true?
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I remember that there was quite an issue about athletes suffering from asthma and other health problems when Russian hackers published the medical records of US and other western athletes that were authorized to use medicines for their diseases that are usually considered illegal doping for healthy athletes.
I did not check who were the athletes in that list that suffered from asthma, but according to this (unrelated) nytimes article "The percentage of all United States Olympians with asthma increased from 1996, when it was 12.4 percent, until 2000, when it was 18.9 percent, according to Fitch. But in 2002, when testing became more stringent, the percentage dropped to 12.9 percent. It was 9.1 percent in 2004 and 12.1 percent in 2006, Fitch said."
In this article from "Die Zeit" in German you can read
Haben Spitzensportler häufiger Asthma? Ja. Asthma ist eine Entzündung der Atemschleimhaut. Ungefähr fünf Prozent der Bevölkerung leiden daran - bei Spitzensportlern ist der Wert teilweise deutlich erhöht. Nach einer Studie australischer Wissenschaftler im Jahr 2012, die die Daten von Olympia-Athleten auswerteten, leiden 24,9 Prozent aller Triathleten an Asthma, gefolgt von den Radfahrern (17,2 Prozent), Schwimmern (17,1 Prozent) und Fünfkämpfern (16,8 Prozent). Auch beim Fußball ist Asthma nicht ungewöhnlich. Beim WM-Viertelfinale 2010 zwischen Deutschland und Argentinien standen acht Spieler im Kader, die eine Ausnahmegenehmigung für Medikamente hatten, unter anderem Mario Gomez.
Do top athletes often have asthma? Yes. Asthma is an inflammation of the respiratory mucosa. Approximately five percent of the population suffer from asthma - in the case of top athletes, the value is sometimes significantly higher. According to a study by Australian scientists in 2012, who evaluated data from Olympic athletes, 24.9 percent of all triathletes suffer from asthma, followed by cyclists (17.2 percent), swimmers (17.1 percent) and pentathletes (16.8 percent). Asthma is not uncommon in football either. In the 2010 World Cup quarter-finals between Germany and Argentina, eight players who had an exemption for medication, including Mario Gomez, were in the squad.
Translated with www.DeepL.com/Translator
You can read here that Froome had problems with asthma and with asthma medication during doping controls (Froome won four times the Tour de France and two bronze medals at Olympic games, among many other things).