Worries about a gear ratio of 1:1? I'm planning a randonneur-like bike with drop bars, STI shifters, and nevertheless some low gears. The crankset could be a "compact plus" (I guess from Sugino), 44 and 28 teeths, and the cassette a normal Shimano 105 11-32.

With this setup, the second lowest gear ratio would be 28/28 = one.

I can imagine that this could add some particular mechanical stress on the the entire rear wheel, from the cassette to the spokes. But on the other hand, given that it's not the lowest gear, I probably won't use it for more than a few minutes in a row.
Should an exact gear ratio of 1/1 be strictly avoided ?

Edit: imagine a cyclist pushing from side to side as she/he stands to climb up a mountain road. As long as the 1:1 gear stays in, the rear wheel always get flexed in the same way.
1:1 and similar ratios are considered bad in automotive gearboxes. If there is one bad tooth it will soon take others with it, if it is always meshing with the same teeth. Automotive gearboxes tend to use coprime ratios (where the 2 gears have no common multiple) to avoid this.

There really isn't a similar issue on a bike. I suppose it might be a good idea to have a prime number of links on the chain to even out wear in case of a bad tooth, but the sprockets never come into direct contact, so that shouldn't be an issue.

Resonance shouldn't be an issue. the resonant frequency of the bike is going to be way higher than your pedalling frequency. It'll be in the audio range. Just give it a tap and you may hear it ring.