Why does a 1300-1400 chess.com player feel stronger than a 1700 lichess player?

Of course the ratings will be inflated, that is because when you have an IM and he plays against a lot of 1800 1900 and 2000 rated players his rating will be a few hundred points higher than his OTB rating. Usually in otb play players are playin against other players who are usually -200 and +200 points than them, that's how you end up with a realistic fide rating. My friend is 2147 fide and he is 2200 on lichess that's very close, why? Well he usually plays against -200 and +200 rated players than him even on lichess. The reason because a lot of people think chess.com player are stronger is that they are cheaters there are a lot of cheaters on chess.com not including titled players every third player on chess.com uses an engine. Chess.com doesn't have a cheater detection option like Lichess does because chess.com is not about learning chess and having fun playing it chess.com is all about money so they don't care about players using engines. Hope this explains a thing or two.

It is interesting how confused the rating system on Chess.com is at this point. As @DunnoItAll stated, most players will have signed on before the option to select Beginner, Intermediate, or Expert was included, and they will in general be underrated compare to what they'd be on lichess.org. Also, now that those options are included, people have the choice of selecting one which doesn't apply to them, which could lead to even greater rating inflation than lichess.org is accused of. The best way to keep a realistic rating, similar to FIDE, is to solely play opponents within about 2 or 300 points in either direction of your own rating, but as close to your rating as you can. This will most effectively mark how much you've improved and most realistically compare to FIDE. On lichess.org it is impossible to enforce any sort of system where you can only play rated games with similarly rated players, and so you can't expect for player's ratings to mimic what they'd be on FIDE most of the time. Also, the difference between the time controls on lichess.org and FIDE hurt the odds that a person will have similar ratings on both, as their standard rating in FIDE will be based on multi-hour games, while their Classical rating on lichess.org may be based on 8 minute games.

The point to all this is that you can't expect one site's or federation's rating system to compare to another's, and there are a lot of factors that go into making them contrast as they do. There is no solution to making lichess.org's ratings accurately reflect FIDE's, and there shouldn't be. A 1000 should be able to play a 2000 in a rated game if they both want. The freedom and accessibility of lichess.org is what makes it better than all the rest.

@Booyakasha Chess.com cares very much cheaters. I had a friend on chess.com who was a diamond member, and still got banned for cheating.

If you're about 1750 classical on lichess you're better than 80% of the pool. But if you were playing in a U2000 tournament you'd be better than 0% of that pool.

@Booyakasha Rating systems don't work that way. In a good working rating system it doesn't matter whether you play against stronger or weaker players because wins against stronger players will give much more rating than against weaker players.
Though it can be that decreasing the time controls lets the skill if stronger players shine more, as they have better pattern recognition etc. so their brains work better under the pressure of blitz. (e.g. Magnus is 2914 in blitz, almost 100 more than in slow)
Also the lower draw rate might help the stronger player (though that's just my personal guess, I don't have data whether that's true).

And as mentioned, "rating groups" aren't comparable if they don't get calibrated against each other which is why e.g. engine ratings aren't comparable to human ratings, or FIDE to lichess ratings etc.

There's perhaps some inflation here due to the free 1500 rating points that new accounts start with, but all in all, I think it's reasonable. My ICC 5 minute rating hovers around 1200-1300, here I'm 1600ish, so yeah. You could say that ICC is a little deflated. My provisional USCF rating is just over 1600. My blitz on Chess24 dropped to around 1550 recently. I think they were fairly inflated there as well in the early days. I was up at 1800 for a bit.

#1

Chess.com initial rating is 1200 and the average Blitz Rating is close to 1100
www.chess.com/leaderboard/live

Lichess.org initial rating is 1500 and average Blitz Rating is close to 1600
en.lichess.org/stat/rating/distribution/blitz

Problems:
Lichess minimum rating is 800 which has an impact of the ratings of all players.
Blitz Time Control on Chess.com differs to Lichess Blitz Time Control.
Lichess uses Glicko 2 with the default parameters, i do not know for sure which rating system and which default parameters are used on Chess.com
Ratings are always more ore less good ESTIMATIONS!!!
The player pool differs (so also the distribution of ratings)!!!

Ignoring all the problems (or assuming they are not very relevant), the most likely estimation (only for average or near average players) should be someting like this:
Chess.com Blitz rating >= Lichess Blitz rating - 500
Chess.com Blitz rating <= Lichess Blitz rating - 300

A 1600 Lichess player is comparable to an 1100-1300 Chess.com Player.

Linear interpolation would give:
A 1300-1400 Chess.com Blitz player is a 1600-1900 Lichess Blitz Player

Your feelings (Why does a 1300-1400 chess.com player feel stronger than a 1700 lichess player?) looks proper ;-)

The usefulness (to me) of the rating system on any site, or for any real-life organization, is to help you pick players close to you in skill, so you have a good game. But I do agree that, in general, you can subtract the 300 points from the lichess rating for CC (that's what I play) to get close to the chess.com rating. That assumes you are not near the very top or very bottom of the range.

I have only little above 50 points blitz rating higher on lichess than chess.com.

my lichess is about 150 pts higher.