I’m a soccer mom: soccer playing kids often wear shoelace covers like these: SweetSpot Band Laces Tied Cleat Covers (All Atheltic Shoes: Soccer, Softball, Football, Baseball, Lacrosse) https://www.amazon.com/dp/B00MRILU70/ref=cm_sw_r_cp_api_glt_fabc_4TT5V0D9HPKDNXDE5671

Should protect your shoes and you can wear them the whole workout unlike some of the suggestions.

Though I would also think you could bring fabric and just cover your shoes before you tighten the straps.

My OTF seems to clean their straps better—I’ve never had this issue. I also always wipe down the straps after I use them.