I was testing some android indie games (showcase) that came out this month on google play and there is one game which made a strong impression on me.

That game was labeled as "family friendly", and after playing one segment of game one must-watch ad pop up, and it was very uncomfortable for me to watch.

I don't want it to be disgusting while describing it, so I'll describe it like half naked(to put it mildly) "girl" which calls user to action of obscenity which is at least not for little kids , just to mention again it's family friendly game and ad was must-watch (the game was the simplest possible (arcade))

Also I remember in the past there was similar ads like experience of adultery(ads for story games, like you are wife and then needs to find you husband kissing other woman(that is in ad))...

I know the game is non-popular so it's "just put first ad system you can find and you will have monetization in game" and it's labeled family friendly because of developer thought that ads don't count or simply didn't knew it, so I can't blame it.

And my question is:

Are there 100% safe ads(for mobile games) which at least don't have those things or I'll have to satisfy me with In-app purchases or to make paid game.

Ads by their nature are going to be a concern when exposed to kids. You could be exposing kids to ads for some cuddly little kitten stuffed toy, a healthy new cereal, and some piece of educational software and you will have complaints about exploiting impressionable young minds. I imagine though that what gets displayed depends on a combination of what the ad company provides, availability of settings to control that on the developer side, and possibly the effects of what ads algorithms think a particular user would be interested in seeing. My advice is to investigate just what kind of control ad services can provide you and see what fits your needs. And if you can, offer the consumer the ability to filter ads appropriately.

As a parent (and I am probably alone in what I do), I try to remember to put my phone into airplane mode whenever I let the kids play which tends to be an effective ad blocker (though not always). I also have not allowed my kids to make in-app purchases, though that's probably worked more because they don't know how to do it. I'm not against the idea of an in-app purchase but I will be the one engaging in the decision and transaction, not my kids.

Game developers here have said for a long time that parents need to be more attentive to what their kids play. I am. Advertisements are a part of that these days, it is just the way of things. My preference is to pay for a game that I know will have no ads and no in-app purchase. But I do still check out free games. I test them out myself and if I think the ads will be a problem and I can't disable them, the kids don't get to play the game. Either way, I am still very picky about what I'll let my kids play at all.

I'm pretty sure the most of the kids don't have any kind of parent advisory , but even without child will choose childish games.

But I don't want "to ruin their childhood even more" with those ads...

So I'm asking here on forum: does anyone have experience with that, because I have feeling there is one ad company which not have those things(or have some options with age limit).

You want to include ads, so I assume you believe they have an effect. If you think they have an effect on people, especially vulnerable ones like children (even if its "just" corrupting them into wasting money), then the logical conclusion is to not include any ads.

Doesn't ad providers allow some kind of customization to prevent direct competition to your app or wildly unrelated topics to show up as ads?

Asking as an illiterate on the matter, but it sounds pretty reasonable that it would allow the ad customisationg go both ways: using the app user's data to customize ads (even if it means showing naughty ones) and allowing the creator to choose categories to focus or avoid.